Sometimes you are not able to check the water conditions before you go fishing. What do you do when you get to the water and find the river or stream level is up and it's looking murky? If it's looking like chocolate milk, then flies are not going to work very well.
If you have the time and means head up river until you find clearer water. The farther you go the clearer it should get. The small tributaries will be the first to clear after the rain, that is if they even got all that dirty. The sediment will move downstream leaving the headwaters clear while the lower river may still be brown. The middle of the system will be the various shades in between. This holds true for most systems, but not all. I have seen rivers that will be dirty up river and clearer down. This is usually due to excess soil erosion in the upper river that does not exist further down. A little rain will muck up the upper river and settle out before it gets downstream. If you get a lot of rain you can bet that the whole river will be off. If the soil was stable in the upper watershed then the whole system would run clearer.
If going up river is too far, than another alternative is to find some small tributaries that dump into the river near your location. These should provide clearer water where the fish can see the fly.
Somewhere in the system you may find that wonderful color in between. Water clarity is just plain ok. It's not clear and it is not dark. This can be the place to catch good numbers of fish and some big ones. Use some good sized streamers and have at it. The fish are less spooky in these conditions and know that plenty of food will be washed downriver. They can't make out your fly real well and will get on it before it gets away. Cast to likely fish holding spots and be ready for whatever comes.
Lets say you are stuck fishing real dark water. Flies don't make a lot of noise unless you are using surface poppers. The fish are not going to move far to get something they can't see or hear. Use the biggest flies that the fish will eat. This usually means a good sized streamer. You'd be surprised how big of fly a fish will try to chomp. My favorite color is black for all species. It has a good silhouette in both clear and dark water.
If the flies are not working you can prick their sense of smell with bait or call them in with the sound of hardware. Sometimes you have to fish the soup or go home.