Herbs freeze well. Either the complete stalks, rinsed, patted dry and separated to freeze quickly on a tray before packaging; or separate (or purée) the leaves, cover with olive oil and freeze in ice trays.
That said, dill is pretty much the only thing that really gets wasted when we get it in our CSA. If I remember to ask ahead of time, often they'll substitute a different herb in our basket. DH won't touch dill, and I can't eat enough for both of us!
Speed comes from what you put behind you. - Judi Ketteler