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. For example, they'll wade 1/4 of the way out into the river and begin fishing. Thus leaving themselves 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". Do not just jump in and start fishing in the spot that you think looks the best. And do not just fish the water directly below where you're wandering. Make your casts into the current then let your live bait or lure flow with the current until it is finally below you, keeping your line as tight as possible the entire time. Repeat this step while varying the length of your casts in order to cover the water entirely.
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 (JRW Gang Hooks are the most natural way to present a worm in my opinion). This is accomplished by adjusting the number of split shot sinkers you add to your line. Start with two and make a cast. If you do not feel bottom through your drift, add another on the next cast and so on. Once you're bouncing bottom, you'll be able to feel it. And with practice, you'll be able to tell the difference between the bottom and a bite with ease.
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 deer portions of the river. Deeper edges and riffles and of course pools are where a major of the fish will congregate (especially in hotter weather.) You do not want to get cooking spending 80% of your time fishing the shallow riffles and 20% of your time fishing the beautiful pool below the riffs. And the deeper edges along most riffles (especially in the bend of the river) are generally more productive as well.
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! My personal preference is a five foot ultra light rod and reel spooled with 4 lb. test. If this would be too "small" for you, a 6 foot light action rod spooled with 6lb. test would suffice, but any larger is complete overkill. If you're going river fishing for fall steelhead, obviously your going to need larger fishing gear. Just make sure to match it to what you're fishing for. I do not need to see any more shark fishermen on my local trout stream.
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." Amen!