fold a length of wire in half and add a bead. (I like to use teardrop shaped beads for the head) Twist the wire just above the bead to hold it in place, later you can hot glue it to keep it there if need be.
Add the rest of the beads for the body, for the second bead I like to use an oblong one to make it look like the first segment of a dragonfly. And I like to use metallic beads for the body. Tie a knot at the end, and wrap the excess wire around the knot.
For the wings I like to use a thicker wire, make a loop and twist it so that it stays.
Make 3 more loops so that it looks like this. Twist it around so that it stays and cut it off from the wire, use pliers to tuck in the last little piece of wire.
To attach the wings to the body cut a thinner piece of wire and wrap it around many times.
To make the wing detailed slide a very long piece of the thinner wire through the wire used to connect the wings and body on the underside, twist it so it won't come undone. Pull it up so it makes a line through the wing and make a loop so it stays.
Keep making loops until it looks like this and then do the same for all four wings.
Then you're done.