step one with working with a GH repo, fork it to your account
step two: clone _your_ repo
step three: setup an upstream remote
step four: create local branch and do your work (just like with gerrit)
step five: push your local branch to your fork, preferably as a branch on your fork
step six: raise PR against the upstream (note: when pushing a branch from your local to your fork the CLI gives you a URL for quickly raising the PR)