You don't checkout a remote (see "Working with remotes"): you fetch from it, and checkout one of its branch:
git remote add coworker git://coworkersUsername/repo.git
git fetch coworker
git branch --all # choose a branch
git checkout --track -b aBranch coworker/aBranch
(See "Working with remote branches")
"coworker
" is the name for a reference to a coworker repo, which is different than "origin
".
"origin
" references the original repo you cloned.
But you can add as many other upstream repos you want/need.