Answer: Deadheading simply means removing spent blooms. The main reasons for deadheading are to prevent seed formation and thereby conserve the plant's energy, and also to make the plants look tidier in the garden. Some perennials and most annual flowers will have extended bloom periods if you are diligent about removing blossoms before they go to seed.
For petunias, pinch or snip off the flower, cutting back to just above a set of leaves. Don't just remove the petals--you need to remove the developing seed pod too. If you deadhead petunias regularly, they will continue to bloom right up until frost.
Daylilies can be deadheaded either daily by removing the individual spent flowers, or you may wait until all the buds on that scape have opened and then remove the scape at the base.
On carnations, cut the whole wiry stem off at the base (leaving the basal foliage) or, if you want to try to encourage rebloom, cut the stem just above a leaf. (The tendency to rebloom depends to some extent on what type you are growing.)
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