Dragonflies and damselflies both create what are called “mating wheels” when they mate. The male grasps the female at the back of her head with the terminal appendages at the end of his abdomen and the female curls her abdomen forward until the tip of her abdomen reaches the male’s sex organs.
Many male dragonflies go to great lengths to make sure their sperm have reproductive success. Prior to mating they often remove any sperm that happen to be in the female from previous matings. In addition, depending on species, they may leave after mating, fly with and guard the female as she lays her eggs, or remain grasping the female as her eggs are laid. His proximity to the female during egg laying prevents other males from removing his sperm.
Much of this information, as well as excellent photos for identifying dragonflies and damselflies, can be found in A Field Guide to the Dragonflies and Damselflies of Massachusetts, by Burne, Loose and Nikula. Another excellent Odonata resource is Dragonflies and Damselflies of the East by Dennis Paulson. (Photo: Mating darners (fast flying, large dragonflies), male above female)