Dragonflies normally are larger than damselflies, and at rest dragonflies usually have their wings spread wide, whereas damselflies fold their wings back parallel with their bodies. Dragonflies usually have eyes close together, and damselflies usually have their eyes separated widely. Both are part of the order Odonata, and dragonflies and damselflies belong to separate suborders, Anisoptera and Zygoptera, respectively. Odonata Central is an excellent online source for information and photos.
The first three species shown are dragonflies, the last two are damselflies. I have posted photos of a couple of these species before, though I hope the pictures here are a little better, or at least in sharper focus, than the previous ones. I took them all in the vicinity of Onion Creek.
Common whitetail female (Plathemis lydia )
An eastern pondhawk male (Erythemis simplicicollis simplicicollis)
Here's a female of the eastern pondhawk
Blue ringed dancer (Argia_sedula)
Aztec dancer (Argia nahuana)
(click any photo to enlarge)