Technically speaking, the correct answer to the question "duck, duck, now what?" is........GOOSE
Anyways I would take the wings (these are great as the wing on wet flies), pluck the flanks really well (a lot of these feathers can be used in traditional style (catskill etc.....) dry flies and the like. If you look near the preen gland (very close to the behind) and remove the feathers covering the soft ones beneath you should find soft, oily feathers that are very "wispy" (for a lack of a better word). These are CDC, or Cul De Canard (fancy french for a** of duck).
CDC is used in all sorts of nymphs, a LOT of dries, even a few streamers.
Those are the main feathers to grab but as DiverDan said just pluck as much as you can of everything. If you don't find a use for it then you wasted a few seconds plucking feathers.
If it's a mallard you are in luck. Great feathers come from those. I have a bag full myself from a locally taken duck.