Add fields to login/register form

I have a ‘login required to view’ site policy and I would like to modify the Register page on the login screen to include more user profile data. In my case, I would like to include the first name, last name and website in addition to just Username and E-mail.

You can see what I mean here:

With that said, I’ve been able to edit the register form itself to include (at the moment) the First name and Last name, but how do I get this user information submitted and stored into the database and viewable in the user profile?

Thoughts?