You will be given a confirmation number when you book and a follow up letter will arrrive 7-10 days later in the mail. You can also check online at the member site and see the reservation there. That will show up by the time you get off the phone with member services. It may not be there for reservations made with developer points - I am not certain how that works but don't think they show up in your online account.
The first two bookings I had the letter within 2 weeks, I booked a room for next august at the 11 month mark and that letter took about 6 weeks to receieve but I was able to see the reservation on the member website, so I wasn't worried.