It auto saves after a mission is complete or you buy something. Whenever you see a small diamond or a big diamond with an exclamation mark on your screen it is saving. You can find a shop, talk to them and then close, it will save.
It should auto-save. Watch the diamond icon on the screen. When it twinkles its saving. Remember that when you go to play Ezio might spawn in a different place than where you turned the game off. It can confuse you to think it didn't save.