I've been to Antelope several times. In 2005 I took one of the tours from a business in Page. They drove us out there, signed us in with the Navajos, then drove up to the entrance of upper. The guide saw me with my tripod and said you better go ahead of the group, just make sure you're in the truck when we leave. He also tipped me off where and when the sun rays would be shining down, and he threw some sand up to help get the quintessential upper canyon sunbeam shot. The drawback to this kind of tour is you don't get a lot of time and you need some time. To get great shots you're going to need to bracket, A TON. So you get set up in a good spot and you'll be there a bit shooting all the different exposures.
The next time I went back to upper in 2006 I drove right out to the entrance and paid straight to the Navajos. They drove me down to the entrance(they do this with everyone, otherwise it would be a decent walk along a very sandy wash) let me go and said when you want to leave come out and catch a ride. This allowed me to spend much more time and feel less rushed.
The drawback to upper in both cases is it's very crowded. Tons of regular tourist firing flashes on their point and shoots wondering why the pic doesn't look like they've seen in the brochure. It's very narrow in places, and you risk getting your tripod bumped by people squeezing past. My favorite was the "photography tour" guide that tried to tell me I had to move because he was leading a photography tour that needed that spot. I've got my 1ds2 and 24-70 set up, I look around and the stoutest camera in the group was a 20D. Half didn't have a tripod, 3/4ths had point and shoots. I didn't move until I was finished.
While I'm thinking of it, get an angle finder, your back will thank you. You will be shooting up at extreme angles a lot and stooping way down to see through the camera.
Lower is like others have said, drive up, pay, and a guy walks you 100 feet over to the entrance. Every so often the guide walks all the way through the canyon, not with you per se, just at his own speed, to see if someone has died, a snake has fallen in etc. Lower is much less crowded with a lot more to shoot, but you don't get the sunbeams. Lower is also ridiculously narrow and twisty in places, but where you'll be shooting it widens enough for people to usually easily pass.
If you have two or more bodies it helps as you won't have to switch lenses. If there's the least bit of wind blowing there will be sandy dust coming down on you.