The main git website is a good place to start learning how to use git, and Github also has a nice collection of guides. I also found this cheat sheet to be a particularly good one-page summary of useful git commands.
To have changes you've made merged into the main repository, prepare them as a patch (
git format-patch) then submit them by email to firstname.lastname@example.org
If using windows, be careful with line endings. Windows tends to change LF into CRLF. They can be changed back using the
dos2unix command in cygwin. Also, make sure the permissions are not messed up (they should be 664)