What You'll Need
Take a dry bag and wetsuit if you know you'll be dealing with water. Wherever you go, take a helmet, harness, rappel device and several carabiners. Take a few slings, which are wrapped around rocks. For more information, check out Climb-Utah.com's Gear page.
Use common sense getting dressed. Quick dry material is recommended, as you'll be sweating and may get wet. Have some warm clothes, too, especially for desert canyons, where an unplanned night in the open can be real cold.
For your feet, ordinary running shoes work, but if you have room in your budget, consider a pair of FiveTen Canyoneers, specially made to provide top notch traction, even in wet conditions. Gloves are a good idea to keep your hands intact while rappelling. You'll need ropes, of course. Check with your guide that you have enough and that they're long enough for your purposes.
Getting lost is a common hazard in this sport, so take a GPS along for the ride. A map and compass are good to have as well. Other items are not specific to canyoneering, but are always good to have when roaming the great outdoors. First aid supplies, a knife, a lighter, some food, lots of water (and a way to purify water) are all good ideas.