Standard Faucets leak from the spigot of the faucet.

Sometimes the pivoting handle can build up debris or  in the valve. If this is the cause for the leaking then cleaning and adjusting the handle height can stop the  leaking.

Turn off the water supply under the sink. Remove the spigot by pulling straight up on the tubing. The spigot sits in the base of the faucet and is only held in place by friction due to two o-rings. Once the spigot is removed the handle will slide off a brass bar by sliding the handle in the direction of the spigot seat or hole. Be careful to not twist the brass bar while removing the handle. Clean the handle and the area of the faucet where the handle was positioned. The brass bar which makes a Tee needs to be raised ½ turn to reduce any pressure the handle placed on the stem valve. (Sometimes the brass bar may need to be raised more but better to try it in half turns increments) place the handle back on and then the spigot. Turn the water back on test to see if the water is leaking. (If the water flow is even stronger, then most likely the brass bar was lowered on the threaded stem rather than raised. Try again.