It's a bit of a risk to try to write about the way of fishing the fly. There are so many "experts" and each and everyone have his own method.
The following is general models that have worked for me in my fishing for trout, char, grayling and put & take rainbows.
Try them if you are a beginner and later develop your own variants that hopefully will give an even better result.
Dry fly fishing
The dry fly fishning is mainly fishing on top of the surface, but sometimes I think you can even put in the fishin in the surface, that is fishing the emergers and hatchers an floating nymphs.
In streams there are a couple of things that mostly must work if you want to catch fish - the fly must float good and high, and the fly must not stripe. This is mostly, but, sometimes a striping fly can be just the thing that triggers the fish. So, if you know there is fish in the water, but it refuse your flies - try the striping dry fly. This will make the fly go anoter way - in the wrong direction. Read more... (n b you will need Adobe Reader to read the pdf file)
Wet fly fishing
Fishing the traditional wet flies has, at least in Sweden, more and more become second to the nymph fishing and dry fly fishing. But, in my opinion, the wet fly with its soft hackle and moveability be outstanding. I never go on a fishing trip without my little box with traditional wets, like Red Tag, March Brown or Black Gnat. Sometimes they have saved my day, specially in grayling waters, like the Gloma River in Norway.
This fishing normaly fits the streams more than the still water. Mostly it means that you cast the fly 90 degrees to the stream and let the fly or flies drift with the water down and in to the bank. Often the fish bite just as the fly change direction when the line stretches after the free drift downstream. Of course you can take advantage of this if you know where the fish stands an straiten up the line so the fly moves just over the place. This is also a good way to fish some nymphs in streams. Read more...
Nymph fishing
Lots of books have been written about nymph fishing, so what can fit into this site is just a little. If you want to get into the subject you have for example:
The nymphs - the larvaes of the may flies - is sometimes the most frequent of the food for the trout. There are a lot of varieties, so of course also, nymph patterns. But several of them can serve as templates covering several species. In this category - nymphs - we often also put in the pupas and larvas from sedges and sometime also the other insects that live in the water, lika hoglouse, scuds, beetles and spiders and so on.
There are a lot written about nymph fishing in theory and practise so if you want to really dive into it - visit the library or a good book store.
Streamer fishing
Fishing with streamers is a little underestimated in many waters, but is often used in put & take waters. You might ask yourself why, because a streamer in the stream often finds the largest fish. Perhaps it is due to the difficulty to practise streamer fishing it in streaming waters.
All fish that prey on other fish can be caught with a streamer or streamerlike fly. The fly fishing for pike and perch is growing, I believe all over Europe. The streamer for trout is classical and in the US you have the search for bass and several sea living fish.
Earlier the streamer was a fly that should look like a little fish. They were tied on long shank hooks with a feather wing - often cock feathers. See the Darters and the Ghost Streamer. Later on, the wings were made from bucktail, and today you use most kinds of hair and also a lot of man made fibres in different colours and with more or less flash.