What's the best way to replace remote.origin.url in Git?

If they already have a remote called origin but want the new remote to be called origin then the most logical thing to do is rename or remove the existing remote called origin and add a new one:

git remote rename origin old_origin

git remote add origin url://new/url.git

If you don't care about the old origin you can just reset the URL, but you would probably want to do a full git fetch and a git remote prune origin afterwards for tidiness.

git config remote.origin.url url://new/url.git

If you have a very recent git (>1.7.0), you have a remote sub command for this:

git remote set-url origin url://new/url.git