How do you keep those David, and your use??
After picking you let them dry (they come off in big sticky green-brown pods) and remove the pods. The nuts store darn near forever until you actually crack the nut.
As far as use, the sky is the limit. In the Middle Ages it was common to store chestnuts and hazelnut as the two could make a rudimentary flour in the event of a poor wheat harvest. In modern times "nut flours" are popular for fancy baking types (like me). That said hazelnut is a common European dessert flavor that has barely bled into the states. I keep touting that I intend to make my own Nutella and maybe this is the year.
There's a lot of cultural stuff that comes with nuts. A Brit might get having a hazelnut scone with cherry preserves with tea or an Italian might use hazelnut for a pesto variation. It just hasn't hit its stride stateside. Don't be sad, they'd be just as lost with a pecan pie with ice cream and a glass of bourbon (which is mandatory after raking leaves).
I grow them because I live in one of the harshest growing climates in the states (USDA zone 3-4) so I take what I can grow. Hazelnut has kinda been one of those weird thingss that has pushed my mind a little. Fun to grow, too.