There is no way that we can cover everything that you need to get started with git. I recommend that you work through the first two chapters of the git book (free and online!). It won't take long and you can skim through sections. This is 95% of what you need to know to use git by yourself. If you read the third chapter you know 99% of what you need to use git in a collaborative team.
Here is a beginner-focussed tutorial we use in another course that focusses on using git from within R.
GitHub is amazing and makes it easy to do a lot with git. In particular it makes it easy to * see diffs, comparing different versions of your project easily, and without having to remember the command syntax. * examine logs so you can see what happened by file, or over the whole project. * use blame to see who changed what line in a file and when. * to help collaborate with other people on code. * use "pull requests", which mean you can easily contribute to other people's projects and they can easily control what is added to their project. * set up continuous integration, so that you know as soon as something goes wrong.
bitbucket is much the same, and both offer educational accounts.