Git is a Version Control System
Have you struggled with combining changes across a team of writers e-mailing edited documents back and forth? Or created dozens of "old", "old2". Yea, then git will make your life better.
If you are course 6, You probably want to read Git for Computer Scientists which will teach you the abstract object model. Nelhage also gives a cluedump in the fall about the object model and you might want to read his slides
But this will not really teach you the commands you need to know for everyday use.
You should walk through The git tutorial for this.
But the real way to learn git is to use it for a project.
At the very least you can just
git init in the directory of any project you start,
git add new and changed files, and
git commit -m "some description of your changes". And pick up collaboration, branching, history editing, and cherry picking when you need them.
There is also the route taken by ezyang and gdb: coming up with some crazy project to do something using git as a tool.