NEWBIE FAQ:
How does one found a religion? Only through a Great prophet. Great prophets can be obtained through some wonders and social policies; however, typically they come from collecting faith points from religious buildings like shrines, certain natural wonders, certain world wonders, and some pantheon beliefs. Once you get enough faith points, you can generate a great prophet. Note however that there is a limit to the number of religions in each game, always less the the total number of civlizations. If you do not act soon enough, you may not get a religion at all.
What are the benefits of religion? There are a variety of beliefs that each adds some bonus. You can see a list here: http://well-of-souls.com/civ/civ5_expansion.html#religion As well, sharing a religion with another civilization adds to diplomatic friendliness.
What are the categories of beliefs? Pantheon beliefs come pre-religion. Founder beliefs (which benefit only the civilization founding the religion) and Follower beliefs (which benefit any city with the religion dominant) are available when you found your religion. When you enhance your religion, you get a second Followe belief plus an Enhancer belief (which expands the potency of your religion). (For a complete list of beliefs, see the link in #2).
What are the best beliefs to select? This is of course game-dependent. The ones I end up selecting most often are Tithe, Pagodas, and Religious Texts. If I start near Jungles, Sacred Path is the obvious choice; if I start near deserts, I pick Desert Folklore.
What is a pantheon? How do I get a pantheon? Pantheons are a sort of “pre-religion” belief. They give benefits to your cities. You get a pantheon by collecting faith points. The more pantheons other civs have founded, the more expensive it gets for you to found one. If you found a religion, your pantheon’s benefits are folded into the religion. It is possible to get a pantheon but not a religion, however, because religions are limited based on the size of the map. Once a religion has been enhanced, no more pantheons can be discovered.
How do I enhance a religion? You need one Great Prophet to found a religion. You'll need a second Great Prophet to enhance it.
Can I change the symbol for my religion from the presets? Maybe with a mod but not in the standard game. You can change the name, however.
How do I spread my religion? Two ways. If you hover your mouse over your cities with your religion, you’ll see a +10 pressure or some number like that. The higher the number, the most likely nearby cities are to adopt your religion, one citizen at a time. The fastest way to spread religion, however, is to spend faith points on acquiring a missionary or acquire a great prophet. Then send these to other cities to spread your religion.
What is a Holy City? The Holy City is the founding city of a religion. For the AI, this will almost always be their capital city. It will generate a lot of religious pressure for a faith, making it the primary center of a religion.
How can I discover what beliefs a rival civilization's religion has? It took me an embarrassingly long time to discover that under "Additional Information" in the top right (to the left of the espionage bar) has a table that gives much additional information about all the religions, including how many cities have been converted to each religion.