Unless you are diving (not literally!) into the world of dragonfly larvae there is little point in looking for dragonflies in Shropshire before the end of April.
Each species has a typical flight period (see species descriptions) and the first species on the wing each year is Large Red Damselfly. There will always be a degree of variation from year to year and should the spring be unseasonably warm or premature then it is always worth casting an earlier eye! At the other end of the season Common Darter is usually last on the wing with sightings typically tailing off toward the end of October. Again should a long Indian summer persist records could be made later. If searching for exuviae then clearly the same time periods apply, however if recording larvae then Spring and Autumn are ideal.
The number of different species observed at a given water body increases towards high summer with the greatest diversity present in July. With species flying at different times throughout the summer several visits to a site are ideally required to obtain a full species list. A far greater challenge however than deciding when to go is planning good Shropshire weather! High winds, cool temperatures and rain are all regular features of a Shropshire summer and all negate dragonfly recording as the insects understandably retreat to the shelter of vegetation. Even the hardened exuviae searcher is thwarted as heavy rains or wind will remove these light structures from the emergence supports. If however all does go to plan the best time to visit a site is during the hottest part of the day between 11am and 3pm.