If you're already running X locally, you shouldn't even need to do anything - if X stuff is being forwarded, just run applications normally and they should display on your local machine. No need to run another instance of xinit, since you already have the server running locally. I don't think the remote machine needs to have X running at all, even. There's a HOWTO
if you want more details.
All you should really need to do is login to a remote machine using ssh - ssh will automatically (should, anyway) set up the right display variables and whatnot; run an X app and it should display locally.