How to theme the register page (mysite.com/user/register) How to theme the register page (mysite.com/user/register). I'm using the Omega theme.

Where do I find the template page user-register.tpl.php ? 

I don't need to add fields to the form, I just to theme this page.
To theme that path via a template file, you can use:

page--user--register.tpl.php

copy page.tpl.php to that filename, clear theme registry cache to apply.

Note, you may need to copy page.tpl.php from your base theme to your sub theme /templates folder to bring it into scope.