My favorite way to fly fish for trout is with a nymph. A nymph is a fly that sinks. The early spring and summer nymphs are generally more effective then top water flies. Trout will lie on the bottom of the stream. Feeding trout on nymphs will rise off the bottom and feed on nymphs and insects.
There are two ways to fish a nymph : 1) without a strike indicator . 2) With a strike indicator (which is a small cork type bobber). When fishing without a strike indicator keep your casts short and the floating flyline out of the water when possible. Watch your line for any hesitation then set the hook. Using a strike indicator makes it easier for the fisherman to spot strikes. Any hesitaion in the bobber means you have a fish. Turn over rocks to get an idea of specifcally what the trout are feeding on. A rabbit hare nymph is good generic nymph to fish (I have found). Try this fly fishing method to help you catch more fish.
(Left picture of a stone hedge nymph)