When one does Tarot cards or other forms of divination, where do the answers come from?

Well, that all depends. Some people believe that the answers are divine in nature and are interpreted through the cards or pendulum or runes or what have you.
Some believe that we see what we need to see. For example, if you are having romantic troubles and you pull the "Lovers" card and the "Death" card, one person might claim this signifies death of the relationship while another that it means an end to the troubles. Granted, each reading would depend on the position of the cards and so on.
Sometimes we already know the answers, deep inside, and we just use divination as a tool to draw them out.

What do you personally believe?

The latter. I believe that we usually already know the answers, somewhere inside of ourselves, and that divination helps us focus and put things into perspective so that we can cull them out.

That is what I think too

Why you... Stop that! Stop thinking what I think! Get out of my head!!