check actions/register.php ... see where the forwarding is done and modify it accordingly.

I'd suggest using one of the plugins that allow you to do this.  Profile manager and Forms and Related Plugins are two that let you do this.

If you still want to do it manually, you'll need to edit the form views in mod/profile/views/default/profile/edit.php and the action in mod/profile/actions/edit.php to accept the new fields.

It's best to pull your changes out into a separate plugin that overrides these views and actions instead of changing the core ones.