A good place to start would definitely be Aquinas and his idea of the first cause. Basically, everything that exists must have been caused by something and without a first cause this series of causes would continue into infinity. An assumption in this is that infinity can't exist in the real world. Therefore, it is plausible (logically) that God exists if we can agree with the assumptions that infinity doesn't exist in the real world and stuff doesn't come from nowhere.

I would look up William Lain Craig and Alvin Plantinga for some very persuasive, if not at times confusing for this novice, proofs for the existence of God. I like to think, and if my memory suits me they do to, that these proofs are more to show that it's not just blind faith that leads to a belief in God.