Start with the dead and damaged branches, because they make the plant look bad, and encourage rot and disease. Also cut out wilted, dried or diseased branches as soon as you spot them, to remove the disease before it spreads. This pruning also thins out the bush, opening its interior to more light and air, which encourages fuller, healthier growth.
Cane-type bushes, such as forsythia and hydrangea, usually send up new canes from their roots every year. In general, prune out the oldest (larger) wood to control the bush height. It’s also OK to trim out newer canes to thin the interior of the plant and let in light as well as to control its spread. If one of these bushes has gotten too big and out of control, you can often cut off all the canes and the roots will send up new shoots. You’ll have a nice new bush in a year or two.
It’s tempting to grab the hedge shears and shape a bush by cutting off the branch tips. This “flattop haircut” approach may look fine for a year or two, but it stimulates growth on the outermost branches, forces the bush to grow into an unnatural shape (your idea rather than the plant’s) and fails to control size. The bush actually grows larger and becomes more difficult to bring back to size without being ruined. The exception is hedge-type bushes.