(based on ArtScroll Siddur)
The enumeration and explanation of the Attributes follows the generally accepted opinion of Rabbeinu Tam, as found in Rosh HaShanah (17b).
(Note: The first two Attributes are based on the two-fold occurrence of the "Name," "Hashem." "Hashem" is really not in itself a Name of G-d; rather, it simply means "The Name." It is used here in place of a particular One of G-d’s Names because we are not permitted to articulate, or even to write, that Name, except for in the Torah scroll itself)
Hashem. This Name denotes mercy. G-d is merciful before a person sins, even though He knows the evil lies dormant in the person.
Hashem. G-d is merciful after the sinner has gone astray.
E-L. This Name denotes power. G-d’s mercy sometimes surpasses even the degree indicated by the name Hashem.
Rachum. Compassionate; G-d eases the punishment of the guilty, and He does not put people into extreme temptation.
ve-Chanun. And Gracious; even to the undeserving.
Erech Apayim. Slow to Anger; so that the sinner can reconsider long before it is too late. (Rav Moshe Cordovero in "Tomer Devorah," describes G-d as a "Melech Ne’Elav," an "Insulted King," Whose subjects disobey Him, yet He maintains their existence.)
Ve-Rav Chessed… And Abundant in Kindness…; towards those who lack personal merits. Also, if the scales of good and evil are evenly balanced, He tips them towards the good.
…Ve-Emet. And Truth; G-d never reneges on His word.
Notzer Chessed La-Alafim. Preserver of Kindness for thousands of generations; The deeds of the righteous benefit their offspring far into the future.
Nose Avon… Forgiver of iniquity…; G-d forgives the intentional sinner, if he or she repents.
…Va-Phesha… …and willful sin…; Even those who purposely anger G-d are allowed to repent.
…VeChataah. …and error; This is a sin committed out of carelessness or apathy.
VeNake. And Who cleanses; G-d wipes away the sins of those who repent.