Find out what the brand of faucet is. Go to a local hardware store, the mom and pop type. Give them the info, they carry rubber washers and replacement cylinders for most brands. Most are great about even telling you how to do the repair work yourself. I worked at one for a couple of years and did this all of the time. Good luck
This link should get you started, Sandy:
Hi Sandy, Buy a good DIY book that has Plumbing repairs for the amature.
Generally a leaky faucet is because of a cracked or broken O ring. If it is a kitchen faucet, you will want to turn off the water and start to disassemble the faucet. You will see the O ring that I referenced as you take it apart. Then bring the old O ring with you to the hardware store to match it up with a new one. Then just reassemble it and turn your water back on.
Don’t forget to use a waterproof grease/lube around the handle if it is tougher to use. You know, works tighter...