You can often get a clue about which plants to deadhead and which to leave alone simply by watching them. If the flowers stay on the plant and become brown and unattractive, it's time to deadhead.
Shrubby Plants with Many Small Flowers
These include Coreopsis, feverfew, golden marguerites, Lobelia, sweet alyssum, smaller mums, Potentilla, flax, Asters, Gaillardia, and Ageratum.
Trimming one flower at a time would be too time consuming, so instead, shear off with grass shears. Get as much of the flower stalk as possible. Avoid buds, but don't worry about taking a little foliage off with the blooms -- it'll grow back.
Shrubby Plants with Large Flowers
These include large marigolds, summer phlox, Astilbe, peonies, purple coneflowers, black-eyed Susan, daisies, annual and perennial Salvia, petunias, and zinnias.
With hand pruning shears (also known as secateurs or pruning snips), cut off each flower individually, getting enough of the stalk so it doesn't protrude awkwardly. It's OK (and in the case of leggy plants, such as petunias, desirable) to take off a bit of the foliage, too.
Not to be confused with pruning, deadheading roses means taking out only the minimum amount of stem to remove the flower.
Make the cut at a 45-degree angle that slopes down toward the center of the rosebush. The cut should be located on a spot 1) that occurs after the first pair of leaves and 2) is directly above an outward-facing stem, that is, a stem that points away from the plant's center.
Long-stem Flowers on Tall Stalks
These include daylilies, larkspur, foxgloves, hostas, tulips, daffodils, Oriental poppies, and irises.
Simply cut back each flower with hand pruning shears as close as possible to the spot where the stalk meets the leaves.
Bloom Longer if Deadheaded
No Need to Deadhead
Sedum 'Autumn Joy'
Most flowering vines
Crocuses and other "minor" spring-blooming bulbs
Wishbone flower (Torenia)