The river is closed to fishing from the first of April to Memorial Day Weekend to protect spawning trout. Mayflies make up the bulk of hatch activity, and any reasonable imitation will usually receive a response when trout are feeding on the surface. Look for trout on current seams and against the banks, and remember that the river's rainbows will hold in very fast water at times. Nymph fishing can be quite straightforward as well, with prince nymphs and hare's ears reliably producing trout. In the early season, try dead drifting a woolly bugger with a prince nymph trailer.
Streamers also work well in the early season with muddlers and sinkers being favored.
A sink-tip line is helpful in getting your fly down to the trout. It seems that everyone ties it differently, so check with area shops for their version of this effective fly. There is regular air service into Hailey, which will put you on the ground next to the Big Wood. Boise and Idaho Falls have larger airports, and both are about 140 miles from Hailey or about a three-hour drive. To reach Hailey from Boise, travel southwest 43 miles on I-84, then take Exit 95 at Mountain Home and go east 83 miles on US 20, finally turning north on SR 75.