In my opinion, the most important thing to remember while river fishing is not to spook the water that you're about to fish. I've seen entirely too many anglers do this very thing. They're standing in the very water they probably should have fished first.
The first tip is: When river fishing, remember to work the area that you want to fish in "sections". Don't just jump in and start fishing in the spot that you think looks the best or just fish the water directly below where you're wading.
The second tip is: When river fishing, while using live bait, the bottom is your friend. As my mentor used to say, "if you're not getting snagged, you're not fishing in the right place!" The goal is to bounce you're live bait off of the bottom as it drifts naturally through the current.
The third tip is: Look for deeper water. For the most part you'll want to spend 80% of your time on any given river fishing trip, fishing the deeper parts of the river. Deeper edges and riffles and of course pools are where a majority of the fish will congregate(especially in hotter weather).
The fourth tip is: Match your fishing gear to the type of fish that your fishing for. I've seen all too many anglers out on my local stream fishing for rainbow trout with gear that would enable them to hook and land a small mako shark!
These tips should save you time, and with any luck, help you catch more fish as well. So get out there and do just that. And remember what a very wise person once said, "a bad day fishing is better than a good day at work."