One of the features of Civilization V: Gods & Kings is the ability to found a religion. Below are the instructions on how to do this:
1 - Once you have constructed a building which produces Faith (such as a Shrine), after earning enough Faith you will be prompted to found a Pantheon. This will give you a base bonus for your civilization.
2 - After you start earning Faith, a Great Prophet will begin to be born in your Capital City.
3 - Once your Great Prophet is available to use, select the unit and choose the top option from their actions menu. "Found Religion" will bring up a new window for creating the Religion.
4 - In the new window, you will be given options to customize your Religion. Once you have selected a symbol, name, and both bonuses, click on the button in the bottom right corner of the window to found the Religion.
5 - Once a religion has been founded, when your next Great Prophet is born you'll have the option to further enhance your religion by following the same method used to found it.
Note: The Byzantine Civilization get a 3rd bonus Religion Bonus slot available to them as one of their leader bonuses.