On the second and third days of Sivan, Hashem told Moshe to tell the Jewish People, "You have seen what I did to Egypt, and how I protected you by carrying you as if on the wings of eagles, to me. If you listen to me, and observe my covenant, you will be for me a treasure among the nations, for the whole world is Mine. And you will be a kingdom of priests and a holy nation! These are the things you should say to the Children of Israel." (Shemot 19:4-6)
When Moshe did that, the People of Israel responded "Everything that Hashem wants, we will do! (Shemot 19:8)
On the fourth day of the month, Hashem commanded that a boundary be established at the foot of the mountain, which should not be crossed all the time that Hashem's Presence would be there. To rise to the level of holiness required to hear the "Voice of G-d," they would need to immerse themselves and their clothes in a mikveh (a fountain used to remove ritual uncleanness).
On the fifth day of Sivan, Moshe rose early in the morning and built an altar of twelve stones for the twelve tribes of Israel. He offered sacrifices and sprinkled their blood on the altar. He read everything that was already in the Torah to the People, to ascertain their agreement, and they responded, "Everything that Hashem wants, "Naaseh V'Nishma," "We will do, and afterwards we will understand!" (Shemot 24:7)
On the sixth day of Sivan, Moshe took the People out from the camp, and they stood at the foot of the mountain.
"And the mountain of Sinai was altogether in smoke because Hashem descended upon it in fire, and its smoke rose as the smoke of a furnace, and the people trembled greatly. And there was the sound of the Shofar increasing and increasing in intensity; Moshe would speak, and the L-rd would echo him in thunder!" (Shemot 19:18-19)
Hashem then told Moshe to warn the People again against breaking the barrier and approaching the mountain. Then Hashem came down to the People, and He spoke to them.
"And the L-rd made all these Utterances, as follows:" (Shemot 20:1)