Deadhead daffodils after they've withered and before the seedpods develop further. The plant's energy will begin shifting to seed production, and you want to stop that process.
The primary goal of deadheading is to foster bulb vigor. It prevents the flower from wasting energy on seed production, ensuring it bursts back strong the following season.
If using your fingers to deadhead, wear clean gardening gloves to prevent infection transfer. Gently grasp the dead flower at the top of the stalk, and give it a twist and a pull.
If you want to use small hand pruners, sanitize them with a diluted bleach solution before you begin, then simply snip the dead flower off just above the top section of the stalk.