To know more about the 10 Commandments, it is best to read Exodus 19 and Exodus 20.
Below is the Jewish ordering of the 10 commandments: See reference at http://www.myjewishlearning.com/article/the-ten-commandments/.
However, the Jewish Publication Society's translation of the Bible, Greek Church Fathers, and most Protestant churches (except the Lutherans), consider that God’s very existence and God’s relation to Israel in addition to the prohibition of worshiping other gods are seen as belonging together, while the prohibition of idolatry forms the second commandment. The Roman Catholic and the Lutheran churches have also another way of dividing the 10 the commandments.
Dual Structure of the 10 Commandments
Though there are no indication of how the commandments were distributed on the actual stone tablets, it is generally assumed that they there were 5 commandments in each of tablet. See http://www.jewfaq.org/10.htm
The 1st 4 commandments deal with human relationships to God. The commandments 6 through 10 deal with human relationships. The 5th commandment is said to be a bridge between the 2 tablets.
My personal note: These commandments are said to be observed in our actions, speech, and thought. It is safe to say that these should be observed in our hearts and feelings as well.