Fantastic trip for canoes or beginning kayakers (or anyone else for that matter).
A recent run taught me a few things: if you stay on the roads up top a Subaru can make it from Garat to Crutchers, there is a 24 hr gas pump in Owyhee (Gas-N-Go), and you don't want to be unprepared out here-- it's very remote.
The shuttle: we used a Subaru and a bike. With careful driving, a Subaru can make it on the roads up top. You will have to lug your gear up and down at both ends, however. This is no small feat. The hike up out of Crutcher is about 2 miles. If the roads are wet, it probably doesn't matter what vehicle you have-- you will get stuck.
Take several different versions of maps. There are few landmarks out here to go by. It took me 8 hours to shuttle and I didn't get lost. I'm not sure what roads you take to get a 23 mile distance for the shuttle (as stated in Amaral), but ours was more like 35 miles one way.
If I haven't scared you away yet, you are in for a spectacular float. Probably the most spectacular scenery on the Owyhee, the EF is stunning. There is plenty of wildlife as well-- otters, beavers, pronghorn, deer, bighorn sheep, golden eagles, and plenty of others to be found.
The paddling itself is pretty easy. Most people will portage both Owyhee Falls and Thread the Needle. The few other rapids were pretty easy. This is mostly a flat water paddle with two substantial portages thrown in.
Groceries and gas can be gotten in Owyhee at the Gas-N-Go. It is a 24 hr pay at the pump, but you wouldn't guess it. Otherwise it's 70 miles or so to Bruneau or 95 to Elko. Take plenty of water, some extra food, at least one full-size spare tire, the whole works. Once you're on gravel you're unlikely to see anyone other than a random cowboy. But have fun. It's gorgeous.
If I had the time, I'd paddle all the way from Garat to Three Forks.