FAUCETS - because of the frequency of their use - are prone to leaks and drips. Most faucets are easy to fix, but you do need to find out two things before proceding to repair the leak. First, what type of faucet you have; and second, where the leak is coming from. Knowing the answers to these two questions helps you identify exactly what needs to be fixed. Leaks coming out of the faucet SPOUT usually result from worn or damaged seats, while leaks from the BASE of the handle usually indicate loose rings.
Regardless of the cause of the leak, you have to disassemble parts of the faucet - which means, after the problem is fixed, you'll have to reassemble them. One of the easiest ways to keep track of the order in which something has been disassembled is to tear off a foot long piece of masking tape, label it from 1 to 15, and lay it lightly on the counter near the sink. This way, you can lay the parts out in the order in which you disassembled them. Then, when it comes time to REASSEMBLE the parts, you can just reverse the order.
When disassembling a faucet, it's a good idea to protect visible parts by wrapping the jaws of the wrench with thick duct tape. This prevents the surface from being marred. And sometimes, no matter how hard you pull, parts just won't come loose. One good way to combat this problem is to spread penetrating oil around the part and wait for about 10 minutes. Keep in mind that some brands of penetrating oil damage rubber parts - so if you use a brand of oil that does, you'll want to be sure to replace any rubber parts as well.
If the faucet being repaired has washers, you should replace the washer with an identical one. All washers have numbers on them to help make it easy to identify the right replacement size - but packages of assorted sized washers are also available. It's also a good idea to replace the O ring - even if it isn't worn out. Instead of spending time trying to work the old O ring off of the valve, cut it off with a utility knife. Then, roll the new O ring down the stem and snap it into place. You should apply plumber's grease to the ring and to any other moving parts of the stem. This helps increase the longevity of the repairs.
Before reassembling the stem, it's a good idea to check the valve seat. If it feels rough or pitted, it'll need to be replaced. But in some faucets, the valve seat can't be replaced - so it has to be repaired. Valve seats can be repaired by using a dressing tool - a little grinding wheel that smooths the seat.