There are 34 species of stoneflies (Plecoptera) in Britain. Stoneflies prefer well oxygenated water associated with rocky rivers and streams and occasionally the rocky shores of lakes. I encountered a sporadic hatch of stoneflies in early spring at Lynnau Gamallt Lakes last year which I was not expecting on an upland llyn. While you can encounter them at any time of year, this is more likely in the spring and autumn.
Stonefly (Nemoura cinerea) Credit 
Plecoptera relative abundance (after NBN 2019)
Stoneflies, the forgotten fly by David Pryce (Salmo Trutta 2005) provides a comprehensive introduction to the group along with a handy species specific calendar of likely flight periods. Rather than attempt to replicate such materials, I would refer you to this guide, included below:
The two life stages that are of interest to fly fishers are the hatching of the nymph and the adult. They go directly from the nymph to adult without a pupal or dun stage. This process takes place at the edge of the waterbody where they crawl out onto rocks or bank side vegetation. While hungry trout may target them during this migration process to the surface and edge of the waterbody it is perhaps of lower importance than the adult stage. Having mated the female will lay eggs in 2 or 3 batches directly onto the water surface. It is at this stage that they are vulnerable to predation by hungry trout.
A few patterns that are worth having in your fly box:
- Small black nymph (12 – 14)
- Spidery brown nymph (12 – 14)
- Realistic nymph (12 – 14)
- Stimulator dry (10 -14)
If you prefer to tie rather than buy:
Tight Lines
Greg