With the exception of some insect larvae that possess true gills, insects that go underwater for extended periods (including all adult insects) must take their own oxygen with them. The diffusion rate of oxygen from water into the insect is simply too slow to support life underwater. There are numerous mechanisms for carrying air underwater including air bubbles and plastrons. In a recent paper in the Journal of Experimental Biology, Pederson and Colmer describe another mechanism for trapping air underwater, the superhydrophobic cuticle.
Insects with superhydrophobic cuticle repel water and the cuticle does not wet. When these insects dive underwater, a thin layer of air is trapped all along the entire cuticle. This thin layer of air serves as a supply of oxygen. In addition, oxygen from the water can diffuse into the thin layer and supplement the oxygen available to the insect.
An interesting example is the damselfly, Erythromma najas, that lays its eggs in the petioles of aquatic plants The petioles are filled with air and provide the eggs with oxygen. To reach the petioles, the female must climb underneath the leaf and stay submerged for up to 45 minutes until the oviposition is complete. The surfaces of the damselfly, including the wings are superhydrophobic and trap air in a thin layer against the body. The surface area, including the wing surface area is quite extensive and provides an adequate volume of air to support the female underwater for many minutes.