To fetch a pull requests by its ID, I probably googled “github checkout pull request” a hundred times by now. Here is a simple Git alias which goes into the .gitconfig to make that a bit easier:

[alias]
  checkout-pr = "!f() { git fetch origin pull/$1/head:pr-$1 && git checkout pr-$1; }; f"

Now it’s just a matter of git checkout-pr 42 to check the changes of pull request #42 on my local system.