How to check if user is logged in, non-vb page?

[sparknote_s]

I know how to program in PHP and interact with mysql so don't worry about that part. I just need to know what files to include() and what variables. Basically I want to do this:

//Check if user is logged in

//If logged in, get username in a variable

And that's pretty much it. It would also be nice if they are not logged in, display a small login box. But that is not necessary, I really need to know how to do the above.

Thanks in advance!