The available date is the day that they'd want you to move in, pretty much. Not that you shouldn't call if you can't move in that day, but every month between the available date and the day you move in is a month that they won't get rent for.

It's kind of a mesh between first come first serve and having an application accepted. For most apartments, there is an application packet. It will want job information, some background stuff, how many people you'll be living with in the apartment, pets, so on. You'll probably need a guarantor, which would be your parents probably, and there will be a form for that.

You probably won't need to call them back, though you may have to play some awkward phone tag when it comes to getting, signing, and returning documents since you're here and not there. You sign your lease and pay those first things (first, last, deposit) when you agree to take the apartment, which could be months before you move in.

If the apartment is owned by a management company, Google the management company and look for people talking badly of them -- this is something that I really wish I did.

If you need to talk about anything, I'm always around :)