Hook: Dai-Riki #135, 16-22
Thread: 8/0 or 70 denier gray or tan
Tail: Brown Hackle Fibers
Body: Olive Superfine Dubbing
Wingcase: Dun Hackle Fibers with Mylar/Mirage tinsel over top
Thorax: Grey Superfine Dubbing
Some of the best patterns are the simplest. The Barr Emerger is about as simple as it gets, but it catches fish. Can be tied in a variety of color and size combinations to cover any mayfly you desire. Can be nymphed deep or tailed off of a dry fly to hang just under the surface.
Here's a video from In The Riffle to get you started.