you don't really specify your starting state. typically if you want to change remotes:
1) commit local repo
2) pull to get current with old remote
3) create a new remote (bare if supported)
4) change remote url to new remote
5) push to remote (with force flags if not a bare remote).
6) test pull
with GitHub you can create a new remote via import of another repo. in this case the client just changes to the new remote
you can check what you current remote is
git remote -v
you can change remote:
git remote set-url origin https://github.com/user/repo2.git
if you local does not have a remote, add:
git remote add repo2 https://myname@github.com/myname/repo2.git