I have the main repo cloned onto my local machine. Before I do anything, I fetch and merge from the origin and then push back to it, so I know my repo is in sync with the github one. Then I fetch the branch I want to merge - usually one that we've got a pull request for. To see what's in the branch:
git log [branch] --not master
This is nice because it doesn't show what's in the master branch of this repo but missing from the incoming branch, it just shows me what's new on this branch.
I can diff and merge at this point, but more than once I've merged and then wondered what changes I have in my repo that aren't in the github one (this is where it is helpful to have fetched from the remote one first). I have the github repo mapped as "origin" as per the excellent documentation so I can just do:
git diff origin/master..HEAD
This shows me the differences that are in my current repo as compared to origin/master, which is the tip of the main repo shown at the version it was when I last fetched it. I particularly use this when I've merged someone's changes in for testing and am wondering quite what was supposed to happen - sometimes just reading the diff beforehand isn't enough, it's only when I get the code merged I realise something unexpected is happening!