Before you begin, there are some things to be conscious of.
Git works most smoothly in a Linux / Unix-like environment. It was first written for use on Linux systems, and still has some expectations that fit best there. This means that if you're running a desktop Linux or OS X, Git and related tools will be easiest to install and configure.
Yes, you can use Git on Windows. Lots of people do, including Lady Ada and (sometimes) yours truly. Just expect that there will be a few more hoops to jump through.
Git is fundamentally a command-line tool. That doesn't mean you have to be a wizard to use it, but it does mean you'll have an easier time if you become comfortable on the command line. Feeling uncertain about this? We've got an entire series on learning Linux with the Raspberry Pi, including guides that focus on command line basics:
There are graphical tools that work with Git repositories, but you will have the easiest time if you install and learn the command-line interface first. Don't worry - it's not actually that bad.
Read on for system-specific instructions.