I'd stick with nymphing to start...the basic nymphs mentioned above will get you fish consistently.
- Pheasant Tails (bead head and non-bead head)
- Plain and Gold Ribbed Hares Ears (bead head and non-bead head)
- Prince Nymphs (bead head and non-bead head)
Fish vertically in holes.
Drift as natural as possible.
Fish two nymphs at a time, one on the bottom and one up (emerging)...i.e. bead head for weight on the bottom, non-bead head up top.
Some guys like using indicators, better to use a big dry fly if you insist on using an indicator...might not represent anything that is actually in the stream, but occassionally can trigger an instinctive strike from a trout.
Ultra clear water, fish lighter tippet.
Nymphing wise, I like around 6x or 7x if they get a little finicky. No need to drop down to 8x unless you are in gin clear water, or facing natives. 6x will give you more abrasion resistance while rolling around rocks.
You should be "ticking" the bottom of the stream with the lower nymph...if you aren't getting snagged some of the time, you probably aren't fishing deep enough.
Good idea to start turning over stones in the rivers you fish, maybe bring a small glass jar with you to take those little creatures (and a little water) back home with you to review. Check out the internet, match the hatch, and find the tied fly/nymph that represents it (and go buy some in a local fly shop)...then you know what to use at the time of year you caught it, what size, what color, etc.
Size wise, get nymphs ranging from 10s to 18s.
Try to match the size of what you find under the rocks!
While other flies/nymphs (matching the hatch) will catch you more fish, the above three will consistently produce fish because they mimic a myriad of nymphs (shape and size). And for most, that is enough to have fun fly fishing!
Good luck [up]