Qantas flies direct to Ayers Rock airport from Sydney and a couple of other airports which aren't on your route (I think Virgin Blue had plans to get started on that route, too, but they don't yet fly it at present, so Qantas still has an effective monopoly - still, their prices for this flight used to be not too over the top). Regular planes (Boeing 737-800s according to wikipedia) with it being a regular airport - just one which only sees very few flights a day, so is rather limited in amenities.
Yulara is a boring resort town, with accommodation for all budgets ranging from really overpriced cabins with bunk beds to a really overpriced 'luxury' hotel.
I'd recommend renting a car at the airport (probably should book that in advance) so you can drive between Yulara and Uluru/Kata Tjuta as the fancy takes you. Fly in on day 1, walk around and see sunset at either Uluru or Kata Tjuta. See the other one on day 2 (personally I found Kata Tjuta to be the more interesting one for exploring). Fly back on day 3 after having done sunrise.
Drink lots and lots and lots of water, especially if you're not used to dry heat and won't feel yourself dehydrating. Buy a silly hat to at least keep the over annoying flies away from your face. And enjoy the amazing scenery! 
[ Edit: Edited on 22-Jul-2009, at 15:35 by Sander ]