GitHub's compare view is available at:
https://github.com/$USER/$REPO/compare/$REV_A...$REV_B
Naturally, $USER and $REPO are the owner (user/organization) and repository names, respectively.
$REV{A,B} are the two sides of the compare view; they can either be a ref in $USER's repository, i.e. the name of a branch, tag or a commit SHA, or it can be a ref in $OWNER's fork of the repository by using the format $OWNER:$REF.
You can get a diff or patch for the result of the compare view by appending .diff or .patch to the URL, respectively.
Examples:
https://github.com/octocat/Spoon-Knife/compare/ed12290ba...master
Default usage is pretty straight-forward.
https://github.com/SomeUserName/Spoon-Knife/compare/master...ForkerChamp:topic/awesome-feature
Branchname is topic/awesome-feature in ForkerChamp's repo.