Familiarize yourself with the various arguments for the existence of God. According to PhilosophyofRelgion.info, these different arguments can be organized under the following categories: the Ontological Argument, the Cosmological Argument, the Teleological Argument, the Moral Argument, the Argument from Religious Experience, and the Pascal's Wager Argument.
Read texts that accompany the various arguments for the existence of God. For example, St. Anselm's text "Proslogium" displays the ontological argument for the existence of God, as does Rene Descartes's "Meditations". The teleological argument, also referred to as the "intelligent design theory" is laid out by William Paley's watch/universe metaphor in "Natural Theology." Read through Thomas Aquinas' "Five Ways of Proving the Existence of God" from his Summa Theologiae, which is often referred to in texts and discourse on the philosophy of religion.
The Standford Encylopedia of Philosophy and PhilosophyofReligion.info are both useful sources for learning about the philosophers behind each argument and provide references to their work.
Explore the historical context of religious philosophies to shed light on a particular theory or philosopher. For example, examine how the influence of enlightenment philosophy in the 18th century influenced the religious beliefs of philosophers and the greater population.
Study how the various theories for the existence of God fit into specific religions around the world. Read the religious texts and doctrine of each religion to find examples of the different philosophical models. For example, explore which theory the Muslim religious model seems to follow by reading the Qur'an.
Place your knowledge of the various philosophies of religion into a modern context, and explore where the philosophies prevail in contemporary society. For example, where does the mystical "Argument From Religious Experience" theory appear in today's modern context? To find your answers you could explore the experiences of Buddhist monks or Christian faith healers.
Explore the philosophies of Atheism and Agnosticism to broaden your understanding of contemporary religious and philosophical discourse. Read the works of authors such as Stephen Hawking and Richard Dawkins to explore different non-religious theories of the universe.