Deadheading

The removal of old or spent flowers is called deadheading. The amount of material to remove is based on the appearance of the plant. The key thing to look for when deadheading is the presence of new buds or flowers. Cut back to something that looks good, like a green leaf. The plant will look best if material is removed at a node or joint where a lead or bud will grow. If the old flower is simply pinched off, a long dried stem will exist up to the next node. When all flowers are spent, the plant can be cut to its basal foliage.

Diagram locations A - D: 
A. OK to deadhead here if no buds are present.
B. Best place to snip if bud is present for blooms to show.
C. Cutting in half after flowering promotes bushiness.
D. Cut to basal leaves when all flowers are spent.

Plants to Shear
Coreopsis verticillata 'Moonbeam' - can be sheared in August to remove deadheads along with the few flowers that may be blooming at the time if needed.
Nepata faassenii 'Walkers Low' - Shear and shape by 2/3 after flowering to keep it from falling over other perennials and to induce lush new foliate and rebloom.

Deadleafing
Hemerocallis 'Happy Returns' (Daylilly) - grab and pull the dead leaves out by hand.
Stachys byzantina - needed periodically throughout the summer to remove rotted or generally declined foliage. Leaves snap off easily with sharp thumbnail. Cut back any large section of the plant that may have rotted.
Some Plants that Do Not Require Deadheading, Deadleafing, Shearing, or Disbudding
Artemisia 'Silver Mound'
Aster novi-belgii 'Purple Dome'
Coreopsis
Perovskia atriplicifolila (Russian Sage)
Sedum 'Autumn Joy'