2 weeks is about how much time it takes. Not always though. Actually, I just requested a transcript from my school last Tuesday and it was completely processed and added to my LSAC file on Monday - 6 days later. Don't except this to always happen, but it just goes to show if you beat the rush, things can move much faster for you.
But to break down how things work for you, you'll send your applications in electronically, and then you'll have to ask LSAC to send your LSAC information to the school. This is call your "report". Unless you have a fee waiver, they cost $12 each/per school. I've forgotten the options of how and when you pay for them. The great thing is, if you're missing your LSAT score, or a letter of rec, or some other non-application part of your file, you can still request LSAC to send your file over...the school will just keep requesting an update until you're complete. And so you know, those updates are free (and you'll see each time they ask for an update on your LSAC file. You'll also see what they get when they request or get your file.)