First, determine whether the leak is coming from the hot or cold faucet. IMM Screw Barrel
Also check whether the water is leaking from the tap or the handle. If it is leaking from the tap, you'll need to replace the washer. If it is leaking from the handle, you'll need to replace the faucet stem or O-ring. Turn off the water at the shut-off valve located just under the sink. Open the faucet to drain out any remaining water. Close the stopper in the sink bowl and place a towel in the sink to protect against scratches or chips.
Remove the decorative top from the faucet handle. Next unscrew the exposed screw and remove the handle. To remove the stem assembly, turn the locknut counterclockwise with a wrench and lift the stem assembly out. If it sticks, try turning it counterclockwise to loosen the stem. At the bottom of the stem assembly is another screw. Remove it and take off the washer underneath.
Take the washer to your local hardware store and purchase an exact match to replace it. If the screw looks worn, replace it with an exact match as well. Clean any corrosion off the stem before replacing it. Replace the washer and screw and reinstall the stem. Put the locknut back on and attach the faucet handle. Replace the decorative cap and turn on the water at the shut-off valve. Turn the faucets on, then off and look or listen for any drips.
Alright! Now youre better prepared for any basic plumbing emergencies that might come your way. For the rest of your home project needs, visit your local hardware store for the tools, products and expert advice you need to start right.