If you really do have no idea where to start, that's not a bad thing! However, I recommend not trying to go create you're own login/registration system unless you do know what to do. Especially if you care about security. This is an extremely easy thing to mess up, even for seasoned programmers. I will be the first to admit, I spent a lot of time rolling my own login/auth modules in PHP, and also spent a lot of time inheriting code where other people implemented their own method, most of the time, improperly.
I recommend learning a web framework. My favorite Web frameworks for PHP are Laravel, and Code Igniter, Laravel being my favorite. You'll find that you'll have a learning curve here as well, but you will find a lot more support for implementing user authentication correctly and securely. For exampe: http://laravel.com/docs/4.2/security
With a framework you could also get lots of helper methods to make DB access fun, easy, and safe. Check out the examples here! You can always use raw sql if you want!, but for your day-to-day CRUD applications, there is no need!
If you still absolutely insist on doing it yourself, though I will warn you against it one final time. I recommend using PDO or MySQLi prepared statements (I prefer PDO).
My guess is that the app isn't too far along since you're still considering how to build login/registration, so you're probably not "stuck" using raw php and doing it all yourself. :)
mysqli_escape_string(mysqli_real_escape_string) is not deprecated. Althoughmysql_real_escape_stringis.