WordPress handles registration with wp-signup.php (in the root of the installation). There are some hooks in place to allow for additional content (such as a signup header, or additional signup fields), but it doesn’t support theming in the same way that other WP pages do.
BuddyPress is a pretty heavy-duty solution if all you want is a custom registration page (so I won’t suggest that you install it on your site), but you might want to check out how it handles registration. Essentially, it provides its own template for registration (which you could do with a Page Template in WP), and then has some functions for handling some of the things that wp-signup.php does inline. See especially buddypress/bp-members/bp-members-signup.php. Using a totally custom registration process like this means that you can do pretty much whatever you want.