Do not leave spent blooms on the plant. Deadhead as soon as the flower begins to wither. This will allow nutrients to concentrate on the bulb. Leave the greenery intact, as it is necessary to make food to supply to the bulb for next year's growth. You can leave the foliage intact until it begins to yellow, approximately six to eight weeks later. If you cut back the flowerless foliage before photosynthesis has occurred, the bulb will not get enough nutrients and will likely die out.
You need to continue to care for your daffodils even after the blooms have faded, as you are essentially feeding and caring for the bulb that will develop next year's flowers. Continue to water as necessary maintaining a good moist soil. Fertilize the bulbs with a 16-16-16 compound.
If you want to go the organic route, sprinkle rich, organic compost around the base of the plants. Be sure that your compost is fully decomposed, as any live plant matter will rob the soil of nitrogen necessary for the daffodil bulb's survival.
Do not fertilize daffodils while they are flowering. Fertilizing during flowering can shorten the already brief blooming period. It may also encourage bulb rot.
Cutting Back the Foliage
Once the foliage has withered, you can remove it by hand. Do not use scissors or a knife as this encourages the spread of virus and disease.