Steps to get started (recommendations from Bram):
Set up an account at GitHub.
You can also have a look at Danae's GitHub tutorial on how to get started.
After having done the tutorial, you might not like doing version control via the command line. You don't have to:
There are many graphical user interface clients for Git. For an overview, see here.
Many software packages we use for coding and data analysis come with Git and GitHub integration. This means that you can run all version control commands via the graphical user interface of these programs. Among others, the following programs include these features: RStudio (for R, see here), PyCharm (for Python, see here), and MATLAB (see here).
If you get stuck, you will probably find the solution to your problem on Stack Overflow.