I have a repository on github with a main branch (master) and a branch for some experimental work. I made some commits and pushed to the experimental branch and everything
To expand on Kent's reply, after you do your clone the only branch you'll have (remotes don't count) is the one that was active in the repository you cloned from -- master in your case.
So, first you'll want to create a new branch to track the remote experimental branch:
$ git branch experimental origin/experimental
and then check it out:
$ git checkout experimental
However, Kent is correct -- these two commands can be combined
$ git checkout -b experimental origin/experimental