Most single-handle shower faucets simply turn water on and off; a pull-up diverter valve on the spout determines whether water goes up or down. Some models, however, have a diverter built into the handle.
Getting the parts
You may be able to find repair parts in a kit for a specific faucet. If not, standard O-rings and washers may fit. In some cases the seal is made with brass parts and no washers; simple cleaning and light sanding may solve the problem.
A corroded diverter stem or one with a weak spring should be replaced. A plumbing-supplies store should be able to order it. Until you have the part, wrap duct tape around the handle of the diverter to keep it from pushing in too far. This will allow you to use the shower while waiting for the replacement part.
Less than an hour for most repairs
Screwdrivers, adjustable wrench, groove-joint pliers
Shutting off water, dismantling a faucet, installing small parts
Shut off the water, close the tub stopper, and place a rag in the tub to catch any loose parts
Repair kit for your faucet model, or O-rings and washers to match