Use Diazinon, Dursban, Oftanol or other product labeled for white grubs. Fairy rings are caused by fungi. They are circular because one spore lands in the middle and grows evenly in all directions. The best solution is to ignore. If thatch is present, control thatch and aerate.
Some turf managers try to mask the green by fertilizing.
Crayfish live in areas occasionally covered by standing water. While they are susceptible to many pesticides, they will continue to reinfest and area. The only long term control is to provide better drainage. In some areas this is not possible. Determine if the cause is shade, poor drainage or poor nutrition.