I'm playing on PC -- so you'll have different buttons, but to get into photo mode while in game, go to the same screen you'd use to see all the general information about the game. On the PC this means hitting ESC, which brings up a lot of general options and info, including the ability to log out of the game. On the PC you press and hold the F key by default to enter photo mode.
I assume there is a similar screen in the XBOX version, and I'd be willing to bet you'll press A (green) or X (blue) to open photo mode.