git pull is really equivalent to running git fetch and then git merge. The git fetch updates your so-called "remote-tracking branches" - typically these are ones that look like origin/master, github/experiment, etc. that you see with git branch -r. These are like a cache of the state of branches in the remote repository that are updated when you do git fetch (or a successful git push).
So, suppose you've got a remote called origin that refers to your GitHub repository, you would do:
git fetch origin
... and then do:
git diff master origin/master
... in order to see the difference between your master, and the one on GitHub. If you're happy with those differences, you can merge them in with git merge origin/master, assuming master is your current branch.
Personally, I think that doing git fetch and git merge separately is generally a good idea.