Sites to start with GIT versioning
My favorite - Bitbucket - Free for 5 users. Priced to scale. I like it because it offers unlimited free private projects. If your project have 5+ developers, than you have to pay.
Unfuddle - paid git versioning service. It have none free plans, only 30 days trail period. Never tried this site.
Repository Hosting - one more paid versioning services. Never tried, also 30 days free trail, none free plans.
How to start with Git versioning?
You can find more tutorials here: http://sixrevisions.com/resources/git-tutorials-beginners/
Or just register at bitbucket.org and try to create your first repository. It's free and has step-by-step instructions how to make it work.
I also recommend downloading SmartGit program, if you do not like command line git interface. SmartGit is a client for Git. It runs on Mac OS X, Windows and Linux. You can get it here: http://www.syntevo.com/smartgithg/index.html