Numbers in [brackets] are the mitzva-count according to the Sefer HaChinuch. Other counts vary.
Yitro, Moshe's father-in-law, hears "all that has happened" to the Children of Israel and comes to Moshe with Tzipora and Moshe's two sons, Gershom and Eliezer. Moshe, Aharon, and the Elders welcome Yitro with great honor. Yitro praises G-d for all that He has done for the People.
[SDT] The straight reading of this portion indicates that Yitro heard about the Crossing of the Sea and of the battle with Amalek. These are the events recorded in the previous sedra. Other commentaries point to certain textual references about Sinai and are of the opinion that Yitro came after Matan Torah, sometime during the almost a year that the People remained camped near Mt. Sinai. If the latter opinion is correct, then we have an example of "there is no set order in the Torah's account of what happen(ed/s)". And we can add the events of Sinai revelation to the list of what Yitro "heard and came".
[SDT] The Torah says that Yitro heard things, came to join the People (to convert to Judaism), and then Moshe proceeds to tell Yitro all that has occurred. Did not the Torah just tell us that he heard things before? Did Moshe just repeat that which Yitro had already heard? Of course, hearing the stories from Moshe Rabeinu directly must certainly be better than catching the reports on CNN. Rabbi Sholom Gold suggests another reason. Our sources say that Yitro came to the People of Israel, not just for a family visit, but to convert to Judaism. If his main incentives for coming were hearing of the wonders of the Exodus, the Splitting of the Sea, and Matan Torah, then his interest in converting might be suspect. Moshe tells Yitro ALL that has happened AND all the travail, the problems that had befallen the fledgling nation. About the thirst and the hunger, the uncertainty. Only after hearing of how "tough it is to be a Jew", would Yitro be able to be accepted into the nation by Moshe. And so it was. Yitro knew it all and still wanted to be part of the Jewish People. On those terms, we are willing to accept converts.
[SDT] Yitro's reaction upon hearing all that Moshe has told him is to say BARUCH HASHEM. The Gemara in Brachot says that we derive the obligation to say a bracha for a miracle from Yitro. The Gemara in Sanhedrin says that it is not a compliment to Moshe and the multitude who came out of Egypt, that they did not say Baruch HaShem "until Yitro came and said it". (The Torah T'mima says that AZ YASHIR was not a bracha but "only" a song of praise.)
On the following day, Yitro observes Moshe judging the People from morning until night. He offers suggestions for a more efficient system. Moshe should teach the People what G-d requires of them, and he should also handle the most difficult questions and disputes. But the bulk of the daily judging should be assigned to qualified individuals who will be in charge of groups of ten, fifty, a hundred, and a thousand people. Yitro explains that this new system will not only make things easier for Moshe, but the people too will be benefited.
(This portion of the sedra definitely seems to have occurred after Matan Torah, even if you want to say that Yitro's original arrival was before.)
[SDT] "On the following day..." The plain meaning would be, on the day following Yitro's arrival. Rashi, however, quotes the Midrash in saying that the day was the morrow of Yom Kippur, that first Yom Kippur when Moshe came down from the mountain with the second tablets.
[Here's a thought] In the big picture, we see that Parshat Yitro with the main description of Matan Torah precedes Mishpatim with its mundane, everyday, down-to-earth laws. Yet at the beginning of Yitro, we find this out-of-sequence portion of the Mishpatim idea. And at the end of Mishpatim, we have the rest of the story of Sinai. So which really comes first - the lofty, spiritual dimensions of Judaism, or everyday life. We can (and should) look at it both ways.
[Point to Ponder] However you look at the first part of the sedra, the story of Yitro seems to be an interruption between the events of the Exodus and the Splitting of the Sea on the one hand, and Matan Torah on the other.
The mood set by Va'eira, Bo, and B'shalach seems to be broken by the mundane concerns of day to day life in the camp and a father-in-law's advice to his son-in-law. What is Yitro doing here?
If you say, this is where it happened, maybe. But it seems as if the Yitro-episode happened after Matan Torah. This greatly strengthens the question:
What is Yitro doing here?
Perhaps the Torah is telling us how to relive the experience of Matan Torah in our own lives. Its suggestion is "be like a convert". Take a fresh view of Jewish life. Marvel at all the things that G-d has done for Bnei Yisrael. Don't take things for granted. Approach your Judaism like Yitro did. Even if you are a Jew by birth, work on being a Jew by choice.
G-d put the dramatic stories of the birth of the nation on hold, to let us take a close look at someone who doesn't have the Mountain poised above his head. Matan Torah was the mass conversion of a family-based group that is attaining nationhood. But the individual still counts. This we can learn from Yitro, the individual.
Moshe accepts Yitro's suggestions and selects the judges. Commentaries point out that the actual qualifications of the judges that Moshe selected were more "modest" than Yitro had recommended. In theory, the very highest caliber person should be sought after as judge. In reality, we often have to settle for the best we can find in our society.
Moshe sends Yitro off on his journey to Midyan (to convert his family - Rashi).
Here's another thought... Assuming that the portion of Yitro's suggestion concerning the system of judges to help Moshe more efficiently teach and judge the people actually happened after Matan Torah (which seems most likely), why does the Torah present it to us out of chronological sequence? Perhaps it is to emphasize to us the role that teaching and justice play as the foundation of our society, upon which the structure of a Torah way of life is able to firmly be built. Without a smooth-running system for everyday life as a society, the Torah would not be able to be properly kept. Mitzvot cannot survive in a vacuum.
Here begins the Torah reading for Shavuot morning. The Torah now returns to the sequence of Y'tzi'at Mitzrayim to Matan Torah. On Rosh Chodesh Sivan (six weeks after leaving Egypt) the Children of Israel arrive at Sinai.
[SDT] The following two observations are famous, but bear repeating:
In the third month following the Exodus, on THIS day, they (the Children of Israel) arrived at the Sinai Wilderness. Why THIS day; THAT day is how you tell a story.
The Torah is not a "once-upon-a-time-a-long-time-ago story book. The Torah is a living guide for our lives, to be constantly rediscovered and relived. Every day, each Jew should imagine him/herself at Sinai receiving the Torah anew. Today we have come out of Egyptian bondage; today we stand at the foot of Mt. Sinai eagerly awaiting the Divine Revelation and today we commit ourselves to G-d and all that He asks of us.
Some say that the custom that some people follow of standing for Torah reading is based on this idea. Just as the People stood at Sinai, so too do we experience anew "the standing at Har Sinai" each time we hear the words of the Torah being read to us.
More significantly, the words of Torah which we learn and live should never become stale. They should be in our eyes as if TODAY we have received them. We should learn Torah and do mitzvot with the freshness and enthusiasm of a first-time experience. This too fits well with the "Yitro model". The challenge: Be a true Torah Jew all your life, for as many years as G-d gives you, but have an enthusiasm that is more common among converts and Baalei T'shuva.
And the other point...
...THEY came to Sinai Wilderness. And THEY traveled from R'fidim and THEY came to Midbar Sinai, and THEY camped in the wilderness, and HE (singular), Israel, camped there opposite the Mountain. There was a level of national unity of purpose that was attained at Sinai that produced a people that was like "one person with one heart". Perhaps that level of unity has never been achieved since then; perhaps it is not possible to ever reach it again. Nonetheless, it serves as an ideal and goal of our Jewish Life and a challenge to repair the rifts in our society. This pre-Torah Sinai experience was something in and of itself, almost independent of Matan Torah that was to follow.
This can be seen in the Dayeinu song of the Haggada - Even if You had brought us near Har Sinai, but not have given us the Torah - Dayeinu, there is sufficient cause for us to thank You. If coming to Mt. Sinai were just to bring us to the place where we would receive the Torah, then the line from Dayeinu would make no sense. But if there was intrinsic value in the experience of camping at the foot of the Mountain - and there was - then there truly is a cause to acknowledge G-d for the experience of MA'AMAD HAR SINAI even without the subsequent MATAN TORAH.
Moshe presents G-d's words to the Elders (and the People), who answer with a resounding "All that G-d says we will do". Moshe then tells the people to prepare for three days to receive the Torah. During this time, the mountain was off-limits. On the morning of the third day, the People gather at the foot of the mountain to the accompaniment of the supernatural sounds and sights of the Shofar, thunder, lightning, and smoke. G-d will speak to Moshe in such a manner that the People will be witness to this direct communication. When Moshe will speak, G-d will answer with a "voice" (and not just via a prophetic vision or spiritual telepathy).
[SDT] G-d tells Moshe that the People should "sanctify themselves today AND tomorrow". It is relatively easy to sanctify oneself on the day of the great miraculous events of Matan Torah. The challenge to each of us is to sanctify ourselves on the many tomorrows that follow. The days after the wondrous events, the magnificent spiritual experiences. The days when our lives return to "normal". This is what being Jewish is about. We sanctify the mundane. Therefore, there really is nothing that is mundane for us.
G-d descends onto Har Sinai (so to speak) and calls to Moshe to join Him. G-d tells Moshe to repeat the warning against approaching the mountain. Moshe then goes down to the people to tell them G-d's words.
What follows is/are the Aseret HaDibrot, the Ten Commandments. They are comprised of 13 p'sukim which contain 14 mitzvot out of the Torah's 613. The Aseret HaDibrot can be viewed as both specific mitzvot as well as "chapter headings" for many of the Torah's mitzvot (e.g. LO TIGNOV is specifically the prohibition of kidnapping, and generally, the category of all prohibitions related to stealing - robbing, burglary, cheating in business, pressuring someone into selling you something that he doesn't really want to sell, moving a boundary marker... and others).
The first commandment sounds like a statement by G-d, but is viewed by Rambam, Chinuch, and others as a mitzva to believe in G-d . It is as if the Torah had said: "Thou shalt believe in G-d". Interestingly, a partner mitzva of this one - the mitzva to believe in G-d's Unity, is also a statement: "...HaShem Echod". Following Rambam's approach, this premier mitzva of the Torah requires us to believe in G-d, to work on that belief by strengthening it and eliminating any doubts that we might have. The mitzva is a full-time, dynamic challenge to continually improve the quality of our belief. (Others see it as an intro to "There shall be no other gods...")
The second commandment contains several prohibitions related to idolatry. Specifically, not to believe in other gods  (this mitzva includes the prohibition of having no belief - atheism), not making idols , nor bowing to them (even without believing) , nor worshipping idols in any manner . Note that this commandment deals with thought and with action.
The third commandment prohibits swearing in vain . This is defined as (1) swearing to the truth of something that is obviously true and well-known - that the Sun is hot; (2) to swear in denial of an obvious truth - that the Moon is made of cheese (interestingly, to swear that the Moon is made of cheese is not considered a false oath nor a lie, since everyone knows that the Moon is not cheese. Only when the truth of a matter is unknown do we use the term lie and false oath. A vain oath is just as serious as a false one, so this distinction is largely academic.); (3) to swear to violate the Torah - that one will eat pork. Such an oath is immediately void since we are considered to have taken a prior oath (at Sinai) to not eat pork. Hence, the oath is in vain and a disrespectful and potentially harmful use of G-d's name; (4) to swear to do something that is impossible - to stay awake for a full week. The common denominator of these types of vain oaths is that they all "cheapen" the use of G-d's name and threaten the smooth functioning of society which often must rely on the seriousness of a real oath.
Commandment #4 deals with Shabbat and contains the positive mitzva to remember the Shabbat with Kiddush , and the prohibition of all manner of M'lacha, specific types of creative activities . The mitzva of ZACHOR includes Kiddush as Shabbat enters, and Havdala as Shabbat leaves. The prohibitions of M'lacha are divided into 39 categories, each of which contains other related activities, usually with the same goal. For example, PLANTING is one of the 39 categories; watering, pruning, and fertilizing all help the growth of plants and are considered TOLADOT of PLANTING.
The fifth commandment is to honor one's parents . Grandparents, in-laws, older (or possibly oldest) siblings, and teachers are included (with differences). Honor of parents is usually considered to refer to that which one does for one's parents, as opposed to reverence (fear) of parents which include that which should not be done because it would be disrespectful.
The second Tablet contains the prohibitions of Murder , Adultery , Kidnapping , False testimony , and Coveting . (Alas, we were hit with the out-of-space problem. Maybe next year, IY"H, we'll start with 6-10.)
The People are awe-struck by the supernatural phenomena and keep their distance. They ask Moshe to tell them what G-d wants rather than hearing His Voice directly. Some commentators say that this request came after the first two statements, "I Am..." and "There shall be no other...". Others suggest that G-d "spoke" all "Ten Sayings" first in an incomprehensible manner and then began "spelling them out" one at a time. After the second statement, the People panicked and requested that Moshe tell them what G-d wants, so that they would not hear "G-d's voice" directly. G-d agreed, so to speak, on the condition that we listen to the word of the prophet, with Moshe as the "chief" among the prophets, and his prophecy - the Torah - having the highest authority.
G-d tells Moshe to remind the People that they heard G-d speak; that they shall make no graven human images (even for art) ; they shall make an altar and offer sacrifices upon it; if the altar be made of stone, its stone shall not be cut with metal tools . Metal implements represent the sword, which shortens life; the Altar represents the lengthening of life. From this rule comes the custom to remove or cover the bread-knife during Birkat HaMazon, since our table is likened to the Altar. (Some authorities say that this minhag applies only during the week, not on Shabbat.) The Altar may not be approached with immodest steps but rather via its ramp.
Parallel to the Torah's account of the awesome experience at Sinai, this passage from Yeshayahu describes his first awe-inspiring vision of angels proclaiming Kadosh, Kadosh, Kadosh. Both sedra and haftara present us with "visions" of G-d's awe, majesty, and holiness.