First, winter can be a great time to fish so it is good to learn. There is peace and quiet on most streams in winter and one can actually catch a good number of fish, including some larger ones. Modern outdoor clothing has been a game changer for me and one needs to wear the best cold weather gear you have. Comfort is key - you can't concentrate on fishing when you are uncomfortable. Also no need to get out early in the morning, so have a nice breakfast, go out late morning and just fish a few hours. No need to push things.
First step is where to go. Fish tend to go to pools with a slight current in the winter and will congregate where it is warmer. This may be a warm water source like a spring or even a power plant discharge or a section of dark bottom. Some of these places may be the cold water refuges in the summer, while others are the places trout avoid in the summer. IMHO, they like to be about 3 or 4 feet down. Deep enough to feel safe, but shallow enough to get some sun. The deep dark pools don't work as well for me. In some winter holes I fish the browns will congregate more in winter than in summer. People are secret about their winter holes, so you may have to move around to find the sweet spots. Biggest issue IMHO is to find out where they are - you need to get close since trout don't move much in the winter.
Trout aren't that hungry and don't move fast in winter which generates two major fly strategies. First is use something large enough to wake them up and make it worth while for them to eat. Streamers or buggers swung slowly near the bottom do the trick here. Cast across, let the streamer sink, and let the current do all the work. Dead drifting is an option. Strikes will often be subtle - more like a leaf hanging up than the savage strikes of May, so strike when you feel anything. I have good luck with both black and white patterns. Buggers are good, but I have also had good luck with Shenk's white minnow (a good dead drifting streamer - looks like winter killed minnows to me) or a Shenk's sculpin.
The second strategy if they aren't hungry is to offer a tasty little snack right in front of their face. Winter bugs are typically tiny, so midge larvae/pupa and little black stone patterns are popular. A small egg, scud, or worm pattern never hurts in my experience either. Of course small pheasant tails, green caddis worms, or hare's ears will work. I have also found to avoid too much flash in the winter. More subtle color combinations work better for inactive fish. Save the flashy stuff for when trout are feeding heavily. In general, I haven't found pattern as important and had a 5 year period where all I used on freestones in winter were LBS nymphs and I caught as many fish as when I brought a large fly box.
Good luck - winter fishing can be a lot of fun.
