I do not know how to, and it does not come automatically. There is no text saying "An update is avaliable, update now?." I know it says something like that because I updated Red Dead Redemption a while ago. Any help how?
As long as you start the game with an online XBox Live account it should prompt you for the update. Check and make sure you don't have it already. If you have it there should be a new entry under "How To Play" titled "What's New".
How to Update Minecraft: Xbox 360 Edition