At the handle while it’s on: tighten the packing nut. Dripping from the spout when off: a worn seat washer. Inside the wall when you turn it on: most likely the faucet burst in a freeze and needs replacing.
Find where it leaks
Leaks around the handle or stem when it’s on
How to tell: Water runs out from behind the handle, around the stem, only while the faucet is open.
Fix: Tighten the hex packing nut behind the handle until it’s snug and the leak stops. If it keeps leaking, the packing inside needs replacing: turn off the valve that feeds the outdoor faucet first, then fit the kit for your faucet’s brand and model.
Drips from the spout when it’s off
How to tell: Water keeps coming out of the spout with the handle fully closed.
Fix: The rubber seat washer at the end of the stem is worn. Turn the water off at the valve that feeds the outdoor faucet before you take anything apart. Fit the maker’s repair kit. If that doesn’t stop it, the seat is damaged and the faucet needs replacing. Worn faucet washers and gaskets are a frequent cause of leaks.
A short drip right after you turn it off
How to tell: On a frost-free faucet, water drains out for a few moments after shutoff, then stops.
Fix: That’s normal: the faucet is draining so it can’t freeze. If the dripping goes on, tighten the handle slightly, without overtightening.
Leaks inside the wall or basement when you turn it on
How to tell: Water appears inside the house, often the first time you use the faucet in spring.
Fix: Turn it off and leave it off. When a hose is left attached in freezing weather, water trapped in a frost-free faucet freezes and bursts the tube inside the wall, and because the burst is after the shutoff, it only leaks once the water is turned on. The whole faucet must be replaced. Find the replacement that fits your pipe.
Prevent the freeze: take the hose off before freezing weather. A frost-free faucet only drains if nothing is attached.