Clamp the adjustable wrench onto the nut that sits directly behind the shut-off valve's handle. Turn the nut clockwise an eighth of a turn to tighten the nut. Turning the nut more can cause damage to the valve.
Close the main water valve in the house, cutting the flow of water to the toilet's valve. Turn on a faucet on a lower floor of the house, if applicable, to release any leftover pressure in the pipes.
Locate the nuts that connect the valve's body to the toilet's water line and the water pipe from the wall. Twist the nuts counterclockwise with the wrench until the valve's body comes completely free. Loosen the packing nut located just behind the valve's handle, then remove the handle, packing nut and the threaded plastic valve stem from the shut-off valve's body.
Slide off the washers from the valve stem and clean with a rag. Flex the washers in several directions, then replace them and reassemble the shut-off valve assembly. Reconnect the valve to the water pipe and toilet's supply hose, then turn on the main water valve to test the valve once more.
Shut off the main water valve again and undo the packing nut that sits behind the shutoff valve's handle. Remove the handle and the valve stem, then install a new stem and washers. Replace the packing nut and handle and tighten the packing nut. Turn the house's main water valve back on.