Once you shut off the water and remove the handle and escutcheon, you can quickly determine whether your single-handle tub and shower faucet is a cartridge, ball, or disk type.
Getting the parts
Tub cartridge faucets work just like sink cartridge faucets. Usually the faucet only turns water on and off; a diverter valve on the spout directs water to the showerhead or the spout. A number of manufacturers make cartridges of varying designs, so take the cartridge with you when you shop for parts. You may need to replace the entire cartridge. Follow the steps remove it.
An hour or two for most repairs
Screwdriver, hex wrench if needed, groove-joint pliers, cartridge puller if needed
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 parts
Cartridge or repair kit for your faucet model, silicone grease
This cartridge works by virtue of its tapered shape, rather than a series of grooves. Note the cartridge's orientation when you remove it so you can put it back the same way. If hot and cold are reversed after you reinstall the cartridge, turn it 180 degrees.