How to log off gmail on iPhone 5?

I signed into my first gmail that I made for my other phone. I put that gmail into my iPhone 5 to transfer my contacts which didn't work. So and all this other stuff and I made another one and I want to use the other one for my gmail, so how do I log out and the one going down your to gmail messages don't work

If it's anything like the iPhone 3GS just go to the email settings and click on your email then push "Delete account". No it won't actually delete it but it removes it from the phone.