$ git remote add theirusername git@github.com:theirusername/reponame.git
$ git fetch theirusername
$ git checkout -b mynamefortheirbranch theirusername/theirbranch
Note that there are multiple "correct" URIs you can use for the remote when you add it in the first step.
git@github.com:theirusername/reponame.git
is an SSH-based URI
https://github.com/theirusername/reponame.git
is an HTTP URI
Which one you prefer to use will depend on your situation. GitHub has a help article explaining the difference and helping you choose: Which remote URL should I use?