That question is a difficult one to answer because your answer is going to vary somewhat from person to person.
With me, the initial account was approved within about 5 days for me, but then there is the verification process where they will call you, send email, and even a piece of snail-mail to verify your personal information. Don't send the snail-mail back to them, or return the call, etc., and they'll freeze your account until you respond.
All in all, I would say from start to finish, I was APPROVED within a week (and from what I have heard, that was REALLY fast.) However, to get the process completed, it took about a month, maybe a little more.