Dragonflies and damselflies both belong to the order Odonata. All
odonates share certain characteristics, including membranous wings, large eyes,
slender bodies, and small antennae. Conversely, there are clear differences
between dragonflies and damselfies.
Look at the eyes: dragonflies have eyes that usually touch, or nearly touch, at the top of the head; damselflies have eyes that are clearly separated, usually appearing to each side of the head.
Look at the position at rest: dragonflies have wings held open, horizontally or downward; damselflies have wings held closed, usually over the abdomen.