It's easy enough, at least for something like this.
The only things you need to know are clone, pull, commit, and push.
Clone is what you do first and only first; it gets the repo set up locally and pulls all the files into it.
Pull is what you use to update your local copy to the latest code on the remote.
You make changes to your local copy, and then use commit to ... commit them, to the local codebase.
When you're done, you push it to the remote and there it is.
There's a few more things - I see they're using a hosted gitlab, so I don't know how they do pull requests really, but usually you just use the web interface to make a fork, then clone from your fork, commit changes, push to your fork, then submit a pull request.