Stiff faucets are caused by worn out parts and the build-up of minerals found in hard water. As the faucet is turned back and forth during use, water gets into its grooves, threads and joints. When the water evaporates, the mineral deposits stay behind. These minerals create friction when the faucet is used, wearing out the parts. You can use vinegar to minimise these deposits, but if the faucet is really stiff, you must take it apart to clean and replace damaged parts.
Look for a manufacturer's stamp on the faucet. Find the packaging if possible.
Take a photo of the faucet mounted to the sink.
Take the brand name, the packaging and the picture to the hardware store. Ask a store clerk to show you to the plumbing section of the store. Ask him to show you where replacement parts for the particular model can be found. Tell him the brand name and show him the packaging and picture.
Purchase all the internal replacement parts for the faucet. You can return the ones you don't need to the store. Purchase a faucet cartridge puller tool. Ask the store clerk to find the one needed to pull the cartridge in your faucet.
Turn off the water line to the sink. The shutoff valve can be found below the sink. If there isn't a valve below the sink, shut off the main water supply to the house. Call a plumber if you don't know where it is.
Close the drain stopper or plug. This will ensure none of the little parts goes down the drain while you're working on the faucet.
Lay out the disassembly or assembly instructions of your faucet on the counter near the sink. Call the brand manufacturer to order a copy if you don't have them.
Remove the screw that holds the handle of the faucet in place with a screwdriver. This screw may be under a removable plastic or metal lid on top of the faucet head or around the side beneath the handle lever. Pry off the lid with a screwdriver if needed. Remove the handle.
Remove the threaded ring cap or horseshoe-shaped clip from the top of the chamber where the replaceable parts of the faucet are housed. Use a pair of pliers or a crescent wrench. Cover the jaws of the tool with duct tape to avoid scratching the faucet or damaging any threads. Remove all rubber seals or O-rings.
Use the specialised puller tool if the faucet has a cartridge and your fingers if it uses a plastic or brass ball. Lift this part out of the housing. Follow the instructions that came with the puller tool if you're using the puller tool. If a ball was removed there will be two small rubber seats and springs -- remove these.
Point a flashlight into the chasm of the faucet to look for broken parts. Pull them out with a pair of tweezers. Spray the chamber with 100 per cent pure bottled vinegar and scrub with a toothbrush to remove all mineral deposits. The vinegar will dissolve the magnesium and calcium deposits. Rinse the vinegar away with clean water.
Compare the parts of the faucet you just removed to the replacement parts. Ensure all replacement parts match the originals. If not, go back to the store with the original parts and find the parts that match. Ask the clerk for assistance to help save time.
Replace the plastic or brass cartridge. Replace the small rubber seats and springs if a ball was removed. Replace the plastic or brass ball.
Replace the retaining clip or ring. Replace all rubber seals or O-rings.
Replace the handle by reinserting the screw that holds it to the faucet underbody.
Turn the water back on and test the faucet by turning the handle back and forth. If it turns smoothly, you fixed it. If it's stiff, you'll need to take it apart again and see if you missed a part during reassembly. Take any new parts you didn't use back to the store for a refund.