The cosmological argument argues that there was a "first cause", or "prime mover" who is identified as God. It starts with a claim about the world, like its containing entities or motion.
The teleological argument argues that the universe's order and complexity are best explained by reference to a creator God. It starts with a rather more complicated claim about the world, i.e. that it exhibits order and design. This argument has two versions: One based on the analogy of design and designer, the other arguing that goals can only occur in minds.
The ontological argument is based on arguments about a "being greater than which cannot be conceived". It starts simply with a concept of God. St. Anselm of Canterbury and Alvin Plantinga formulated this argument to show that if it is logically possible for God (a necessary being) to exist, then God exists. Which basically means god exists when he/she/it wishes too.
The argument from degree, a version of the ontological argument posited by Aquinas, states that there must exist a being which possesses all properties to the maximum possible degree.
Quatum physics tends to agree.
Arguments that a non-physical quality observed in the universe is of fundamental importance and not an epiphenomenon, such as Morality (Argument from morality), Beauty (Argument from beauty), Love (Argument from love), or religious experience (Argument from religious experience), are arguments for theism as against materialism.
The anthropic argument suggests that basic facts, such as our existence, are best explained by the existence of God.
The moral argument argues that the existence of objective morality depends on the existence of God.
The transcendental argument suggests that logic, science, ethics, and other things we take seriously do not make sense in the absence of God, and that atheistic arguments must ultimately refute themselves if pressed with rigorous consistency.
The will to believe doctrine was pragmatist philosopher William James' way to prove God by showing that the adoption of theism as a hypothesis "works" in a believer's life. This doctrine depended heavily on James' pragmatic theory of truth where beliefs are proven by how they work when adopted rather than by proofs before they are believed (a form of the hypothetico-deductive method).
The argument from reason holds that if, as thoroughgoing naturalism entails, all of our thoughts are the effect of a physical cause, then we have no reason for assuming that they are also the consequent of a reasonable ground.
Knowledge, however, is apprehended by reasoning from ground to consequent. Therefore, if naturalism were true, there would be no way of knowing it—or anything else not the direct result of a physical cause—and we could not even suppose it, except by a fluke.