Being a lover of macramé, chinese knotting and also knitting, I tried to combine all these skills into one and came up with a knitted and knotted dragonfly.
I’ve made a few of these and they’re very popular. I did not invent these little creatures, they're a traditional chinese knot, and this is only one (easy) way of making them.
I use a knitting nancy/dolly and two strands of cotton yarn or wool, or one strand if it’s thick enough, and knit about 1.8 metres of it (180cm).
The thicker the cord, the more length you’ll need.
You could also use 2 needles to knit the i-cord (Tutorial here), I'm not sure which way would be the quickest.
If you can't stand the idea of knitting so much i-cord, there are knitting mills available (Inox), but they only take relatively fine yarn, and so don't make very sturdy cord which makes better dragonflies...
It's better to knit a bit too much rather than too little of it, as you can always uravel a bit on each end after you've finished knotting you dragonfly.
You can add a couple of beads for the eyes, they need to have a fairly large hole, though...
Finally, there are a few tutorials for the dragonfly knots online, the best one can be found here http://whatknot.tripod.com/knots/dragon.htm.
If you're new to macrame or knotting, you should practise tying a square knot, so have a look at this explanation.
When you've finished knotting, just hide in the ends from the right and left cords in the middle of the dragonfly.