Several manufacturers make single-handle cartridge faucets. Each model has a cartridge of a slightly different design. A cartridge may have a cylinder with grooves or it may be tapered so water can pass through when it is turned.
Getting the parts
If water leaks out the spout, you'll have to replace or repair the cartridge. If a leaky faucet's cartridge is plastic, replace it; if it's metal you may need to replace only the O-rings. If water wells up below the handle, replace the O-rings around the faucet body. Many repair kits contain both the cartridge and the O-rings.
Less than an hour for most repairs
Screwdrivers, hex wrench, stem puller
Shutting off water, dismantling a faucet, installing small parts
Shut off the water, close the sink stopper, and place a rag in the sink to catch any parts
Replacement cartridge or O-rings and seals, silicone grease