Leaky faucets are no good at all and should be taken care of promptly. A leaky faucet will get corroded and will waste a lot of water, and will cost you money.
Steps needed to repair a single level leaky faucet.
You will need a repair kit.
Slip joint pliers
On a one handle kitchen or bathroom faucet there will be a ring that needs to be loosened under the faucet handle, and all the working parts are inside the unit.
Turn the valves off under the sink and turn on the faucet to let the pressure out of the faucet.
Remove the handle with a hex wrench, this will be in your repair kit, and the screw may be under a plastic emblem on the handle.
Loosen the ring and take the top off.
There will be two channels; one each for the hot and cold water. These channels will have a spring and a washer in each. There should be replacement springs and washers in your repair kit.
Get a repair kit with a replacement ball included, these are best to replace as they can get scared.
Put it all together and turn the water on and try your new and improved faucet.
Without major complications the faucet should be like new.
Steps needed to repair a leaky two handled faucet are;
Figure out which side is leaking by turning one valve at a time off under the sink.
Take the handle off by removing the screw that fastens it to the sink. The screw may be located under a plastic cap in the handle use a sharp object to remove the cap.
The valve will screw out and there will be a washer on the underneath that will need to be replaced.
Install everything back into place and try it out.
On this type of faucet I have found that sometimes it is best to replace the whole faucet. It seems like once the washers start wearing out; they are very hard to get repaired, and to work properly for very long.
One thing I have found on some of my plumbing jobs; cabinets under sinks that are so full of stuff that the homeowner would have no idea if the plumbing was leaking for years or not. After digging through years of cleansers, dish washer detergents, pots, pans, plastic bags, and bug spray it is clear that the bottom of the cabinet has rotted out due to a leak.
I would highly recommend keeping your sink cabinets cleaned out and organized and looking under them at least once a month.