Hopefully I don't sound smug or seem like I'm bragging in any way here, but some guide friends of mine and I have noticed that many if not most people we guide just don't wade well. Our proficiency is probably mostly just a result of time spent in the river but here are some things to think about and to try when you venture into or across fast water:
1) Keep yourself turned to the side with your feet spread in heavy current. Water pushing on one leg, rather than both, will exert a lot less force and with a wide stance and most of your weight on your downstream foot you'll be able to lean into the current and stay on your feet.
2) Take a kind of a practice step first to test the footing before actually stepping and putting all your weight on one foot. This will help you to find and stay off of unstable rocks.
3) From experience - don't fish and wade at the same time. Unless you really can do 2 things at once this is just a bad idea. Just concentrate on wading while you wade, then stop, and then fish - works out better I promise.
4) Carry, and use, a wading staff. I have to say "and use" because I've seen people with wading staffs neatly folded up in their cases go for a swim. The best wading staffs for convenience and ease of carrying are the telescoping or collapsible variety.
5) Wear the best footwear. Felt soles are ok on freestone streams but for all purpose fishing, hiking, and serious wading I love boots with Aquastealth rubber soles. Go with Aquastealth soles and studs for maximum traction. Be wary of other "sticky rubber" that may turn hard. It won't provide the same kind of traction in the long run. Almost all good wading boots come with felt, Aquastealth, and studded options for soles. Korkers have interchangeable soles so you can get all of these options for use in different situations.
6) Actually practice wading. For many fishing situations it is actually better to wade less but when things are slow practice walking on round rocks and in moderate currents.
7) This is the most important one - fish more! The more time you spend in the river the more natural it will become.
See you on but hopefully not in the water.