Comprise means to include. It's more formal that consist.
Compose, for the purposes of juxtapositioning it against comprise, means to make up. It also means to write or create.
Think about parts versus the whole
When you use comprise, you put the whole first.
Example: A year comprises of twelve months.
When you use compose, you put the pieces first.
Example: Twelve months compose a calendar year.
If we look at the picture I used to accompany this post, we could describe it in two ways:
The puzzle comprises of 100 pieces.
One hundred pieces compose the puzzle.
If you can just remember that the whole comprises the parts, and the parts compose the whole, you've got it made!