Hello. I am a new gardner and want to properly care for the plants
in my new yard. We have Mexican Heather planted in the front and
I understand that it is a perennial but I cannot find what I am wanting
to know in any of my gardening books. I need to know if I am supposed
to cut it back or what. It still has all the dead leaves on it. Can you
recommend any book that may answer questions like this?

I don't know where you live so I can't give specific advice on this native of Mexico.
Here is Texas it requires little or no trimming. Depending on where you are, the plant may have been hit by a hard frost in which case it may have died back partially or entirely.
Tony M