Determine the location of the leak. Note if it is leaking from behind the hydrant handle or out the spigot end. A leak from the spigot end usually indicates a worn-out washer. A leak behind the handle may be an issue with the hydrant stem.
Turn off the hydrant's water supply. The valve for the hydrant is typically located in the basement.
Open the hydrant's handle to release any residual water once the water supply is off. Remove the hydrant head with a wrench or pair of pliers.
Take out the hose washer by first removing the screw that holds it in place. Clean out any grime or debris where the washer sat then replace it with a new washer.
Apply plumber's grease or Teflon tape to the stem on the hydrant then re-install the hydrant head.
Turn on the water supply and test for leaks. Repeat the above steps if necessary
Heat up the supply pipe to the hydrant. The safest way is to wrap the pipe in electric heat tape and check it periodically. Otherwise, you can use either hot water or a blow torch.
Remove the hydrant head and washer, after turning off the water supply, if you'll be using hot water to thaw the pipe. Place a funnel in the mouth of the pipe and pour hot water down it. Re-install the washer and hydrant head once the water flows freely again.
Hold a blow torch far enough away from the water pipe to heat it, if you go with this method, but avoid holding it close enough to damage the pipe or fittings. Start with a low flame held 4 to 6 inches away from the pipe. Increase the flame volume and proximity if needed. Make sure your work area is well-ventilated and do not use a torch in an area where gases may be ignited or near gas appliances.
Re-apply heat, as needed, until the water supply is restored.