GitHub has a lot of neat features but this has to be my new favourite one.
If you're looking at a pull request, example at https://github.com/simon-reynolds/url-magic/pull/1 you can quickly view the diff by going to https://github.com/simon-reynolds/url-magic/pull/1.diff
If you want to download the patch you can simply go to https://github.com/simon-reynolds/url-magic/pull/1.patch as well
These links will show the diff and patch for the pull request in it's current state so if another commit is pushed the diff and patch will include them
If you want to download and apply the patch to a local copy of the repository then it's the command line to the rescue once again
curl -L https://github.com/simon-reynolds/url-magic/pull/1.patch | git apply -v