When a dahlia blossom has passed its prime, removing the dead flower head will encourage the plant to produce new buds and help control pests and disease. This activity of clipping off spent flowers is called deadheading.
If in a hurry, simply nip off the flower heads. Otherwise, use scissors or pruning shears and cut back to a main stem. This will stimulate new growth and longer stems that are better for cutting.
For more information watch our VIDEO on How To Deadhead Dahlias.