Curt, to your first question about the weather: expect a November average of 60 for a high, to 28 for low, with about 1 inch of rain for the month, and lots, lots of sunshine. So, take a hat for the sun and layers and use the internet for last minute weather updates (try Kanab, UT).
Trail conditions begin with hiking thru /along the Wire Pass tributary of the Buckskin.....most of the time a dry desert wash....unless there has been a major storm. Then the trail to the Wave is sand and Navajo sandstone slickrock. Sticky approach shoes/boots. Walking stick (mono-pod). Trail to the Wave from the Wire Pass parking is perhaps 3-1/2 miles and about 2 hours. The BLM has been sending along with your permit a really great 4-page map "Coyote Buttes North - Finding the Wave" in recent time . It is all you will need for the Wave. If your permit did not come with this, get back in touch with the BLM. With the map finding the Wave shouldn't be a problem. Take care that going in you take visual "go-back" benchmarks as you'll be leaving at dusk and it's easy to get off trail. I've done it countless times and I still get a little return-route question.
Suggestions for essential things to take: Fashlights. Shoot the Wave with sunlight, but the rest of Sand Cove is special with the end-of-the-day light, and if you are dedicated you will be walking out in the dark. Need a led head lamp to trail light, and a 100-yd light like a Surefire G2 to see ahead.
Extra Preparation: AAA's "Indian Country Guide Map".....essential for road navigation in the four corners area. USGS 7-1/2 minute topo's: Coyote Buttes and Poverty Flat. And if you really want to explore the area: "Hiking and Exploring the Paria River" by Michael Kelsey.
Logistical suggestion.....where are you staying? Suggest Lees Ferry Lodge at Vermilion Cliffs (1-928-355-2231) as a base camp. Maggie Sacher runs the lodge and is the focal point for the whole Arizona Strip. Great nearby photographic stuff.
Photographic suggestions: the Wave is, well, THE Wave. And a zillion before you have taken the shot. So do it. Then climb up 100-yards to the base of the cliff. Reflecting pools. Then traverse the contour line southward for about a half mile. Wondeful views down into Sand Cove. Along the way is the "Second Wave." Take care with the boot-steps as this terribly fragile sandstone needs to be there for those that follow you.
Hope this helps,
Mike Coffey, Prescott, Arizona