Thomas' arguments were not considered proofs of the existence of God in the scientific sense (because belief in God involves faith) but in the sense that believing in God is a rational step. (See related link)
There are five 'ways':
1. The argument of Unmoved Mover
2. The argument of First Cause
3. The argument of Design and Purpose (Teleological)
4. The argument of Degree
5. The argument of Contingency