Thank you very much. I just did not really know how I would like, connect the database with my website. Does that even make sense? Sorry!
PHP and MySQL work very nicely with each other. There are tons of tutorials out there for learning how to connect them, it's pretty easy.
Trying to develop a whole social networking site on your own though... that's a big task. Of course, you wouldn't need all of the options of Facebook or anything like that.
As NogDog says though, just because you run it off of a database doesn't mean that you have to allow users to sign up. I ran my video game site as an invite-only site for years before I made it public.