At this time of year, you can expect to find hazelnuts, sweet chestnuts (not to be confused with inedible conkers), acorns, walnuts and beechnuts.
Most nuts will fall naturally, so once you have gathered them up and removed the husks, they will need to be dried out ready for storage. Place them in a dry, shady area, with good air circulation. Once dry, freeze them for 48 hours, as this will kill any unwelcome bugs.
Chestnuts, unlike most other nuts, do not need to be dried and should be frozen straight away.