If you want a guided trip I would look into booking a seat on a comercial guided trip such as Gates of Lodore (green river) or the Yampa. Both of these trips start in the state of Colorado (Dinasaur National Monument) and finish in Utah.
The commercial trips have space for 20 or so clients and 4-5 pro guides rowing the rafts. Some outstanding scenery for the whole trip with lots of good side hikes. On a commercial trip all you do is set up your own tent each night and the guides take care of everything else. Both of these trips have enough white water in the class III and IV range to make them exciting yet safe. You can book a commercial trip with just a few weeks/days lead time.
If you are more interested in a private trip you could apply for a river permit lottery (deadline for permit application is Jan/Feb for trips the following spring, so this years permits are already filled.) If you hold a permit you can find LOTS of folks that would join your trip and act as guides. A post on the Buzz would result in dozens of skilled boaters willing to help ouit.
You don't need any river experience to be the permit holder, but someone in the group needs to act as 'Trip Leader' and have the required skills and background. Private trips cannot involve payment or fees outside of the shared group expences (hence the private vs. commercial permit types.) You can always return the permit if you can't assemble a group.
Here is somemore info on permits Western river trips... lots of good pic's too.
rivergeek western river permits
Ladore, Yampa, Westwater, Dolores, Ruby/Horsethief all start in Colorado.
note: Dolores has a narrow window of good water flows and may not run at all in a drought year.