Wikipedia has a wonderful article on these amazing creatures, quoted in part here:
"Female dragonfly lay eggs in or near water, often on floating or emergent plants. When laying eggs, some species will submerge themselves completely in order to lay their eggs on a good surface. The eggs then hatch into nymphs. Most of a dragonfly's life is spent in the naiad (that is, nymph) form, beneath the water's surface, using extendable jaws to catch other invertebrates or even vertebrates such as tadpoles, fish, etc. They breathe through gills in their rectum, and can rapidly propel themselves by suddenly expelling water through the anus. Some nymphs even hunt on land, an aptitude which could easily have been more common in ancient times when terrestrial predators were clumsier.
The larval stage of large dragonflies may last as long as five years. In smaller species, this stage may last between two months and three years. When the larva is ready to metamorphose into an adult, it climbs up a reed or other emergent plant. Exposure to air causes the larvae to begin breathing. The skin splits at a weak spot behind the head and the adult dragonfly crawls out of its old larval skin, pumps up its wings, and flies off to feed on midges and flies. The adult stage of larger species of dragonfly can last as long as five or six months."
"Dragonfly." Wikipedia, The Free Encyclopedia. 4 Aug 2009, 02:02 UTC. 4 Aug 2009 <http://en.wikipedia.org/w/index.php?title=Dragonfly&oldid=305932692>.