Damselflies are easy to photograph, so long as you can spot them they tend to settle in one place quite happily while you snap away at them. Dragonflies are a different kettle of fish completely. There is a trick to photographing dragonflies tho, they are territorial and fly in a circuit.
What I find easiest to do is put the camera on manual focus – auto focus will never work for these fast movers – then set your camera to where you know the dragonfly is going to hover albeit briefly, and when it shows try and get it in focus and shoot. If you miss it the first time don’t move the camera or the focus, just wait for it to return and try again.
These dragonfly images were shot hand held as I didn’t have a tripod with me, however if I had the opportunity I would definitely be using one. Dragonflies are hard work but they are addictive to shoot. You just know they are going to be back again and you might get a better shot! One other thing… dragonflies and damselfies are only out when the sun is shining, so there is no point in looking for them unless it is a bright sunny day.