The tatting pattern for this dragonfly can be found at DSD9 Designs. At this site you can also get the kit to make the dragonflies. The instructions below are shown using the self closing mock ring (SCMR) method. You could also use the split ring method (which I prefer because I love to tat split rings). You will need 1.5 yards of thread and two shuttles.
Step 2: Hold the threads as shown with a loop at the bottom. Assume that Shuttle 2 (brown) is your ball thread and use shuttle 1 (with flowers) to make the chain stiches.
Step 3: This is how I hold my threads.
Step 4: Make your first chain ds using Shuttle 1 (with flowers).
Step 5: After making 3 chain ds, slide one wing bead into place and make the 4th ds.
Step 6: Continue with one more ds and slide in wing bead 2 and make another 3 ds.
Step 7: Make a loop for a ring using Shuttle 2 (brown) with 2 eye beads within ring thread.
Step 8: Make 2 ds, slide one eye bead in place and tat another 4 ds (as shown above). Slide 2nd eye bead and tat 2 more ds.
Step 9: Close ring (photo above) and continue to chain: 4 ds, wing bead, 2ds, wing bead and 3 ds. See photo below.
Step 10: To close SCMR, slide Shuttle 1 (with flowers) through loop and carefully close the SCMR by pulling the Shuttle 1 thread.
Step 11: Chain 12 ds for tail. Tie knot and cut.