The sound of dripping in the bathroom is doubly annoying when you realize how much water the drip is wasting. If you count 20 or more drips per minute, you're losing almost two gallons of water per day. Persistent dripping also stains the sink. But it isn't difficult to stop, especially if the faucet has a ball-valve, which almost all Delta single-handled faucets do. The springs and seals in these valves wear out under normal use, and you can replace these yourself by disassembling the valve. The manufacturers designed the faucet to make this easy for a homeowner to do.
Turn off the shut-off valves under the sink. If you have a vanity cabinet, you'll find them inside it, on the back wall. Turn both of them clockwise as far as they'll go, then turn on the faucet to drain it.
Unscrew the handle with an 1/8-inch Allen wrench and lift it off if the faucet has a lever-style handle. The screw is usually hidden behind a plug; use a flathead screwdriver to pry off the plug. If the faucet has a plastic knob, pry the plug off the top and unscrew the handle with a Phillips screwdriver.
Unscrew the cap underneath the handle by turning it counterclockwise. You may be able to do this by hand, especially if you wear a rubber glove. If it's too hard to turn, wrap the glove around it and turn it with adjustable pliers. Pull up on the valve stem to remove the cam and ball from the valve housing.
Pry the rubber seal out of each of the inlet holes in the bottom of the valve seat with a pencil. The seal is attached to a spring which should come out with it.
Wipe the inside of the valve seat with a cloth and check the ball. If it's full of mineral deposits, they may be causing the drip. Soak the ball overnight in white vinegar to dissolve them.
Replace both springs and seals. Insert a new spring into a new rubber seal. The spring is cone-shaped and the small end goes into the seal. Fit the seal around the tip if a pencil, then use the pencil to push it into the inlet hole.
Set the ball back into the valve and fit the cam over it. Fit the tab on the cam into the notch on the housing and push down. Screw on the cap by hand while pushing down on the valve stem to keep the ball seated.
Loosen the adjustment ring to make the stem easy to operate, then turn on the water and open the faucet all the way in the mid hot/cold range. If water leaks from the stem, tighten the ring until the leak stops.
Screw on the handle and push on the plug with your fingers.