I mainly fish the Eastern Sierra and for late winter into early spring, the name of game is baetis. This means BWO's (blue-winged olives) for dry flies when the hatch is on and something along the lines of a pheasant-tail nymph or Barr's emerger with an indicator when fishing wet. Sizes range from 16 to 22, though smaller is usually more productive. The stones don't really show up until April and May.
Midges are also popular, such as WD-40's, Serendipities, Optimidges and Zebras.
As others have said, streamers (e.g. Wooly Buggers) are always a good option, especially when nymphs won't work and nothing is rising off the surface. When the trout begin to spawn streamers are great, as the spawning trout hit them out of aggression. Streamers are also easy to cast for the beginner. Although they are heavy and ungainly in the air, as long as you can get them down stream and retrieve them along and undercut bank or through a pool, you will usually get a strike.
All of these are fairly broad-use patterns, at least where I fish!
Good luck and stay with it! It's tough on beginners, but you're in a great place for fly fishing.
ERG
ERG