The flies are made from white craft shop foam about 1/16" thickness. It's best to cue up and do several at a time. Cut a strip of the foam about 3/8" wide. An Exacto knife and metal straight edge is a good way to do it. For a #10 size hook, cut the strip into 7/8" long chunks. Scale proportionately for larger and smaller hook sizes. Take a chunk and cut it to a trapezoidal shape by making diagonal cuts along the side so that one end is left 3/8" wide and the other is about 3/16". Next make a bevel cut about 45 degrees on the 3/16" end. Finally fold the end together at the bevel and nip the corners off. This gives a nicely rounded body end. The hook is going to be inserted through the foam and the foam folded around the hook and glued in place. I use a gap filling cyanoacrylate glue such as Zap-a-Gap. It seems to help the sticking quality to prime the foam on the side opposite from the bevel with the glue by putting a drop on it, spreading it around with a bodkin and setting it aside to cure. The bodkin gets crudded up with the glue from this, but can be easily cleaned by scraping with a razor blade.

The tail is made from a mallard flank feather dyed the right color.  Cut the center stem where the barbs are about right for the tails. About 1/4-3/8" down from there cut the stem again and peel away all but two barbs on each side so you get this pitchfork looking tail structure. Glue the handle part of the tail to the 3/16" end of the foam so that the concave curve is up with respect to the side to which you glue it.

Start the thread at the eye of the hook and take it down to opposite the barb. At
this point make about a 6" loop of thread and lock it in place as if it were a dubbing loop. We will lace the fly with this. Take the thread back to within 1/3 of the shank length of the eye and set up a post of elk or deer hair of the right color for the fly and tie in a hackle alongside the post to be wound parachute style later. Take the thread back to the eye.

Punch a hole in the foam about in the center of the piece. Take the hook out of the vise and push the foam piece onto the point and around the bend, glue primed side to the hook and put the hook back in the vise. Put a drop of cyano glue on a piece of paper and pick up some with your bodkin and lightly coat the front part of the foam piece--it's important not to get too much glue or you'll get it on your fingers and have other problems. Pinch the foam around the hook shank, enveloping the post and hold for 20-30 seconds until the glue sets. Be careful to leave the hook eye and a little bit of shank exposed. Now coat the back half with glue and lay the loop you made earlier down the centerline. Pinch and hold this part of the foam closed until it sets, capturing the tail and the thread.

Now lace the body with the loop sticking out the end with a series of cable hitches spaced about 1/8" apart to get the segmented body look. A cable hitch is a half hitch made such that the thread comes out underneath, providing a measure of self-locking. If you want to be really obsessive about it, recall that mayflies have ten body segments. Do this up to just behind the post. Between hitches the thread should lay along the top of the body. As you apply and tighten the hitches, the body will curve upward, nicely imitating the real thing. A crocheting hook is a very helpful tool for making these hitches.

You could make a final hitch in front of the post with the loop, but it's easier to make this segment with the tying thread which is there at the front. You can anchor the loop by putting a drop of cyano glue on it with the bodkin, wrapping a turn or two around the last hitch on the body, and hold it for five or ten seconds. So make that final segment in front of the post with the bobbin and then take a wrap around
the post and let the bobbin hang. Wrap the parachute hackle around the post in the standard way--top to bottom--and then take two or three wraps of the thread around the post through the hackle to secure it. Finally take the thread to the eye and whip finish or anchor it with a drop of cyano glue. Trim the end of the hackle and paint the white foam body with a Pantone pen of the appropriate color, and you're done. A word of warning--don't take the shortcut of painting with Pantone before you glue. The Pantone ink seems poison the glue so it won't set.