Dragonflies and damselflies are closely related. Once you know what to look for, telling the two members of the order Odonata apart is easy. Look for evidence in these four details: eyes, body shape, wing shape, and position of the wings at rest.
Dragonflies have much larger eyes, taking up most of the head as they wrap around from the side to the front of the face. The eyes of a damselfly are large, but there is always a gap of space between them.
Dragonflies have bulkier bodies than damselflies, with a shorter, thicker appearance. Damselflies have a body made like the narrowest of twigs, whereas dragonflies have a bit of heft.
Both groups have two sets of wings. Dragonflies have hind wings larger than the front set of wings. Damselflies have wings that are the same size and shape for both sets, and they also taper as they join the body.
Finally, Dragonflies hold their wings out perpendicular to their bodies when resting. Damselflies fold their wings up and hold them together.