When looking for Dragonflies/Damselflies, it is best to go on a hot, sunny day. 
A cool overcast day can be very disappointing. 
An interesting spot for the summer hawkers, especially brown hawkers.
RSPB West Sedgemoor is a reserve purely for wildlife and hence you can't actually go into the reserve, you can walk along the drove bordering the reserve.  It is this drove which can be interesting for feeding dragonflies, as well as a good spot for butterflies and possibly seeing or hearing the odd common crane messing around in the fields or flying overhead.
It's a place to visit later on in the year and doesn't seem to have any action early on.
Hawkers love the drove for feeding.  You'll see them flying around trying to catch bugs etc.  If you watch them long enough, they may well land in the hedgerow, you hope it is at a point suitably located for a photo, more than often it is not.
The best place I know for Brown Hawkers and seeing them is normally not that bad, taking a photo is something else.

Later June / July / August
DRAGONFLIES: Brown Hawker, Southern Hawker, Migrant Hawker, Ruddy Darter, Common Darter

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

Route
Park in Swell Wood.
Then walk down the steepish narrow lane towards West Sedgemoor, watching out for the odd vehicle that uses the road.
Once you've got out of the overhanging tree, have a look in the field on the left-hand side.  I've seen loads of hawkers flying around and feeding just under the tree line, but it can be a bit hit or miss.
Carry on down the road, you'll go through high hedges.  Quite often, there can be hawkers feeding between the hedges, or resting on the hedges.
Once down the bottom of the road, I tend to walk right along the drove, which can be muddy and is uneven.  I would imagine the drove is 2 or 3 miles long.  You can walk along there until you've decided you've had enough, noting it is the same distance back.  You just turn around then and walk back.
Brown Hawkers along the drove tend to find a feeding area and stick to it.  If you don't see them for a while, they probably are resting and resume their hunt after a rest, or after they have munched whatever they have caught.

Small steepish tarmac road down to West Sedgemoor, very uneven track at the bottom.