The above posts are good and there are some solid books that cover river smallmouth basics. But to add my .02...
Spring is really feast or famine depending upon conditions. Stable, clear water, almost regardless of river level, can be great. You can get on numbers or catch big pre-spawn/spawn females. The big thing is understanding that they're looking to feed like crazy before spawn without spending a ton of energy. In consistent water conditions, look for quality feeding areas near spawning locations (good current breaks with access to gravel and weed beds). Pre-spawn fish are super aggressive and will move towards smaller water like mouths of feeder creeks or protected areas like gravel beds/weed beds to spawn. There are a ton of posts on here about bed fishing. Bed fish are typically males. Females (much larger, usually) will be sitting off, either in protected areas recuperating, or staged right on the weed lines/current break/change in depth most closely located to where you're finding the spawning beds. You may not catch a ton of females the closer you get to the spawn, but you have a great opportunity for some really big fish.
Post-spawn is a weird in-between stage where you might begin to catch earlier spawners moving towards summer patterns, while other fish may be lethargic for a few weeks after they spawn. Lethargic fish, in a river, will always seek to escape current in comfortable, typically lower, water temperatures. For those fish, it may mean deep, or it may mean protection behind points, near weed beds, or large pieces of cover. These are not typically easy fish to make bite. The ones moving toward their summer patterns, however, can definitely be caught, and will likely be moving towards the seems of faster current looking for baitfish or crayfish. I don't spend a lot of time fishing heavily protected areas. The aggressive fish are likely to be right on the seams. I like crayfish patterns year round, but I absolutely love crayfish patterns during this period.
Summer means higher water temps, lower oxygen content (in some rivers, though it's not nearly the same as in lakes. Current, wind, riffles, etc all help to oxygenate the water). Active Fish can be found basically anywhere with good current, but larger fish are going to be found in better feeding areas where they can eat a ton without struggling in the fast stuff - usually. (Predator dominance typically dominates feeding locations on any body of water, and river smallmouth are rarely the exception.). Fish, once they start to really recover following post-spawn, will typically feed really heavily because this is their primary growing season and they need the food to fuel growth and their metabolism in the warmer water. Almost anything goes, depending upon conditions and where you're finding fish, but I like walking baits, poppers, crankbaits, spinnerbaits, flukes, grubs, football jigs(craw trailer), and tubes to cover most conditions. Also, on hot days, in hot water conditions, don't be afraid to dead stick prime locations. I'm working hard to improve at this, but guys like Jeff Little absolutely crush summer smallmouth this way. If you aren't familiar with him, and want to learn rivers, follow his youtube videos, buy his DVDs, and even his subscription videos can be really good. He's probably the most analytical river fisherman you'll find, and he's very articulate.
Fall can almost be two separate periods, I think. Late summer into almost mid-fall can be incredible. Water is typically low and fast, and fish put on their feed bags once the water starts to cool so they can bulk for the winter. This is pretty similar to the summer, but the fish tend to have put on weight, and as their forage grows, matching it becomes a whole lot easier because (in most rivers I've fished) they're eating essentially everything. Every river, again, is a bit different, but generally, any place with ambush opportunities, good current, and current breaks is in play. Weed beds, boulder fields, points are all good, and even better if they provide some deep water access nearby. That said, long runs and flats with good boulders in a river with a big crayfish population can be absolutely money. Basically bring everything in your entire tackle box. Almost anything that can be fished where the fish are holding can produce fish. What kinds of patterns? Hellgramite, madtom, perch, crayfish, minnow, shad, shiner, sculpin, goby, mayfly, stonefly, refrigerator magnet, lug nut with a treble hook, miniature garden gnome - it almost doesn't matter so long as you can make it wiggle and get them to chase it.
Late fall is when things change, for me, and tend to really slow down. Fish start moving towards protected wintering areas, so areas that transition away from fast current and more towards moderate current can be really good, but it's important to slow down more towards a winter pace. The water is getting colder, and fish metabolism is generally slowing down. Protected points, oxbows, protected areas behind islands, etc can all be good so long as they provide relative deep water access. This time of year for me, is tricky, and I might be doing everything from dead sticking big suspending jerk baits, to digging for the most finesse stuff I can dig out of my crate. As the water cools, this is a time of year I really miss real pork chunks being available.
Winter. Metabolism is slow, fish are generally inactive (barring a warm spell. They will turn on for this and you should be on the water if possible. Fish can move shallow and actually be pretty aggressive). During this stretch, hair jigs, silver buddies, dead sticking, etc are your best options. I don't get out often in the winter (ice and nasty river conditions beat me up pretty bad), but what I've learned is that fish will relate in the most protected areas possible - meaning away from current and deep enough to avoid predators like birds. They can be tough to find, but when you find them, you'll usually find a ton of fish stacked up in the same place.
Year round notes:
High water (and this will happen all year) will typically push the fish to the bank or behind large current breaks like points. Low water can have them feeding on breaks or the heads and tail outs from pools or boulder fields within the pools. Low water will concentrate fish in prime feeding areas near/in fast current/. High water will disperse them to areas with protection from current like flooded areas, behind points, into docks, stack them against the bank (especially if there are trees or boulders/rip rap to hide behind) , push them behind islands, or even settle them into deeper water where the current is much slower than the surface if they don't have access to any of the above. Smallmouth are very heavy sight feeders and like clear water, high visibility, and even sun (way more than largemouth). This means clear to tea stained water can be great. Chocolate milk - go home and read a book.
I'm sure I'm not the best river smallmouth fisherman on the forum, but I've been doing it for a long time and if I were to paraphrase my experiences and a bunch of books, this should cover 80% of the conditions you'll run into.