There is nothing wrong with Daniel Pittman's solution, however, I would consider these mergers as "not fast forward", i.e. changing step 3 for:
git checkout ${target_branch} && git merge --no-ff ${remote}/${branch}
Using --no-ff , the story will be easier to read. He will clearly say that $n makes transactions from $branch , and it will also make your life easier if you need to return something in this branch.
To answer the eoinoc question and give additional advice:
After the merge is completed, your git cli will prompt you to write a message, as a rule, a general message will appear saying something like
Merge the remote "user / branch" branch into your branch
Be sure to edit this message and include a link to the pull request number. That is: (Assuming the pull request number is 123)
Merge the remote "user / branch" branch into your branch
refs # 123 to solve something ...
So, the next time you go to the github issues / pull-requests page and check for this particular pull request, you will see your message with a link for fixing where you merged.
Here is a screenshot of what I mean.

Guillemo Mansilla Nov 25 '13 at 4:50 2013-11-25 04:50
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