Use your eyes
This rather bland piece of advice can create success for most fly fishers.
Fish actually show themselves more often than most people think. And I don't just mean fish that jump out of the water with loud, obvious splashes on a mirror smooth surface, but also small whirls in a riffled surface or shadows over the bottom on a sunny day.
Use your eyes and be on the lookout for movements in the water - even in rough water. More than a few fishers imagine that you can only see fish touching the surface when it's quiet, but not so. Even when there's foam on the top, you can often see your quarry when it moves.
The key is to look for differences and variations: a quiet swirl in randomly turbulent area, an odd splash in a calmly moving surface, foam or sprays in soft waves. All these and more can be indicators of fish under the surface. Even fish moving half a meter or 1-2 feet down in the water can stir the surface. Don't count on a 10-lbs. fish underneath, but it won't do any harm to cast to the spot. The splash can be a coincidence, but you might as well fish to a splash than any other random spot.
If fishing slows down or comes to a complete halt and no movement is seen, go sit on the bank or beach and watch the water. Leave it alone for 10 or 15 minutes, and you will be surprised; often a fish will show in the spot where you were wading just a minut ago.