The nymph of the damselfly is by far the most important stage to the fly fisher. The trout eat damsels from shortly after ice-off until it is too cold for me to fish. When tying flies to imitate the damsel I would suggest you make a well-defined head and be sure to represent the caudal lamellae or three pronged tail. Those combined with a tubular shaped body and legs should do the job. Color should be a darker green (olive) in the hatching season. Color should be a light green in the fall months and decrease the size of the fly.
I have seen various methods to try to imitate the swimming motion of the damselfly nymph. Wiggling the rod tip with a dry line and a very short leader, fluffy flies that undulate with short pulls, etc. I don't feel that any of those methods have worked very well. My most successful method has been to 'still fish' the damsel. I let it sit as if it were resting between swims with an occasional movement to attract attention. I almost always use a dry or floating line for this approach. Sinking lines tend to get hung up in the bottom vegetation too frequently or you have to retrieve too fast. Try a weighted fly for down deeper or a non-weighted fly for near the surface.