You probably realize that many books have been written about this. I highly recommend spending the price of a handful of flies, $15, to order the Handbook of Hatches by Dave Hughes. Covers a lot of ground on the bugs trout eat and the dries, wets, and nymphs used to catch them.

Try using a dropper ... tippet tied to a dry fly's hook bend with a small nymph on the other end. Try a Hare's Ear, Prince, Pheasant Tail, or Sparkle Pupa (for caddis) perhaps a hook size smaller or so than the dry. May have to play with the tippet length, but try to get the nymph close to the stream bed.

Cast across and upstream of the trout to give the nymph time to sink. Dead drift the rig, let it swing downstream, and when it reaches the end of your line, give the nymph a moment to rise to the surface, much like a natural.

For streamers, try bead head Woolly Buggers or Muddler Minnows. Dead drift them around structure along the bottom. Watch the line for subtle takes. Let them rise at the end of the drift. Can also hand strip these in.

Try some bead head flies. It's like cheating. You get to use a jig when fly fishing.