Finding Current User

I’ve put a login box right into index.php, but what I’d like it to do is check to see if someone is already logged in and if so simply say “welcome, username” and maybe have a couple links to sections of the admin area. Thing is that I can’t figure out what variables to access to find out if the user is logged in and if so what their username is. I imagine it’s a session variable or a cookie, but I can’t find it documented what exactly to look for.