When looking for Dragonflies/Damselflies, it is best to go on a hot, sunny day. 
A cool overcast day can be very disappointing. 
I need to explore Exmoor a lot more for Dragonflies as I know there are lots of spots up here worth going to.  
Pinkworthy Pond, well it's really a reservoir, is probably one of the best and contains loads of the more unusual species that Somerset has, including Common Hawker, Black Darter, Keeled Skimmers and Emerald Damselfly.
It's a stunning spot, but can have wild swimmers, or activities going on from the nearby activity centre.
Also, being at a higher altitude, its season tends to start later on compared to the Somerset Levels.
Pinkery Pond is at the source of the River Barle and the start of the fabulous Barle Valley.

Later July / August / September
DRAGONFLIES: Emperor, Common Hawker, Black Darter, Keeled Skimmer, Golden-ringed
DAMSELFLIES: Emerald Damselfly, Common Damselfly

NB The list above just names the key species during these dates and is not a complete list.

Route
Located about 3 miles west of Simonsbath.
You have to park in the various parking areas on the side of the road near the entrance to the Pinkery Centre of Outside Learning.
It is then a 20 to 30-minute walk up through the Barle Valley to reach the reservoir, via a public footpath.
When walking up, you enter the Activity centre via a gate.  The area just after this gate has a small concrete bridge over a stream.  Have a look around here for keeled skimmers and golden-ringed. I'm also pretty sure I saw a small red damselfly around here, my only sighing of one in Somerset.
You'll arrive at the reservoir on the east side, go down to the bottom and have a look around that area.  Also, have a walk along the western side of the reservoir as well.  There is a nice rocky outcrop at the far end.  To get there you'll either need to wade through a very swampy area, or take a longer route around.

Tarmac road up to the Outside Learning Centre, then a grass track, which gets more uneven the closer to the top you get, generally all uphill up to the pond, some steepish sections.