I've never had a dog since I've been boating but I've seen plenty of dogs that were brought to the river and expected to just hop in the boat and go for the ride. Sometimes it works however I've seen lots of dogs run on shore and trash themselves trying to keep up with the boat, or completely flip out when the boat hit a riffle or rapid. Merritrd's advice is the best thing I've ever heard about how to train a dog for the river - by conditioning them to be familiar with the boat, the PFD, and the environment and especially the commands.
I'd also add that others have said it really helps to go for a flatwater float first with the dog, then work up slowly to bigger and bigger rapids.
Nothing in the world is more yielding and gentle than water. Yet it has no equal for conquering the resistant and tough. The flexible can overcome the unbending; the soft can overcome the hard. - Lao Tse