There are 15 companies that provide excellent multi-day raft trips through the Grand Canyon . These trips range from 1-15 nights in length. On all of them, you will be camping along the river and escorted by professional guides who will do everything from cheerfully educate you to cooking you delicious meals. All of these companies (which are private enterprises) are licensed by the National Park Service and have excellent reputations for safety and service. They all offer slightly different trips in regards to craft type (motor, oar, dory or paddle rafts) and meeting/return locations.
Some offer half trips where you can hike 9.5 miles down or up the famous Bright Angel Trail to join or leave a trip. And some go all the way to the end of the Grand Canyon at river Mile 277, some even helicopter out or in at river Mile 186, or drive out at Mile 225. Even fewer offer one night at a working cattle ranch on the rim and one night on the river between Mile 186-277. Which company you choose will most likely depend on which one has the tour offering that best fits your schedule, interests and abilities.
To get more information about the different Grand Canyon rafting options you may wish to visitOutdoors Unlimited, Arizona River Runners, raftgrandcanyon.com, Hatch River Expeditions or Western River Expeditions. To save yourself some legwork, you can find your trip through Flagstaff-based Rivers & Oceans; they work with the commercial river outfitters in the Grand Canyon. Their service is free.