Moved to Guide at species level.

Neon Skimmers will perch long enough for a shot if you give them their favorite angle of perch. They like a slanted perch above water (I use skinny bamboo stakes--a bundle at the Home Depot garden center isn't expensive--though they'll also use tree limbs.) The slant can be fairly steep. I've got one perch that's had a Widow Skimmer and a Neon Skimmer male on it at the same time.

A telephoto lens really helps--I use a zoom--and patience. If you can put in a little pond, with some vegetation (they also really like water iris as perches), or plant iris or other strong-leaved plants near the water, they'll probably use those, too. The only ones I've caught in flight have been females hovering while they lay eggs.

For dragonflies, a digital SLR is probably the way to go. You'd want a sharp, fast telephoto that focuses close, but in bright light, even a standard telephoto will do. It's easier and faster to focus, and the shot-to-shot time is faster.

Don't get me wrong. I love my Nikon Coolpix S10 for most insect photography, but it's rare for me to get a dragonfly with it.