Lots of good advice on this thread...if I had to summarize where to place a fly, I would say to place it where the water is moving at "medium" speed...in other words, not in the white water, and not in the slack water. I find that the fish like to concentrate in feeding lanes where the water is moving at a certain pace - fast enough to drift the food to them, but not so fast that they cannot maintain their position in the stream. Sometimes, you're lucky enough to see them rise all the way from their holding position - all they do is tilt upwards, which brings them right up to the top, they sip in the insect, then return back down to their original level, downstream of their original position. It is almost perfect economy of motion, with no wasted effort.
Now, each pool will have at least one, and some several, feeding stations. My favorite place to put down a fly is at the head of a pool, just to the side of the main flow. Usually, there is a pocket of slower moving water at this point, and inevitably there is a trout there. If the fish are rising, and you can present your fly without drag, you'll get a hit. However, make sure you fish the entire pool, from the tail end up to the front. In the small streams I like to fish, I'm usually just flipping it out there - I only have a few inches of flyline hanging off the end of my rod. In some cases, I'm only casting leader, and I'm holding all but an inch or so of leader off the water.