Soft hackles and wet flies are the most productive fly for the amount of water covered overall. You can get long drifts and swings with little time casting. From the time the fly lands in the water until you pick it up the fly is effective, so stay alert at all times. Wet flies can stand in for many different fish prey. Mayflies, Caddis (all life stages) and minnows are all represented. Also other flies like streamers and leech or crayfish patterns are effective with this method. Almost any pattern that you care to tie on will likely serve you.
Speaking of Caddis, using a floating pattern such as a elk hair dry, and skating or skittering it across the surface of the water is a very effective tactic. you can use it to cover a lot of water and the fish will spot it from quite a distance. It is a method that works best in tails of pools, but don't limit it to that location. It will help you locate fish in unfamiliar water.
Another fish locating method is the Streamer. They are great for locating fish in unfamiliar water. Cast toward logs, larger rocks and other cover. Retrieve in short little jerks and move to new locations constantly. Vary your retrieve as well. There are only certain fish in each location that will fall for a streamer, and covering a lot of water is essential. But if you find one, the likelihood of finding several in that location is quite good. If you get a follow but miss, mark the location. You now have the address and can come back later with another fly.
With dry flies, look for feeding fish, or cast only to the most productive looking water. Don't try to cover all of the water with a dry as the drifts are usually much shorter than with other flies, and you will waster valuable time casting. Walk along the stream until you find a good looking piece of water, about 2 feet deep or less, and with good current lanes next to slack water with some fish cover. Alternatively, work the riffles which often harbor feeding fish.
The same tactic applies to nymph fishing. Choose riffles or well defined runs and deeper cuts. Get the fly down to the bottom with a bead-head pattern and drift it through. Don't try to prospect for fish with nymphs as other methods are more productive.
Practicing these tips and flexibly incorporating them into your angling repertoire will up your game.