To repair a leaky shower diverter valve, it is necessary to replace the part. Replacing the valve is not an expensive or difficult project, and it is not necessary to turn off the main water supply.
The first thing to do is to find out what type of attachment the spout has. If there is a small hole or screw under the spout, cover the drain, and then use an Allen wrench, sometimes known as a hex key, to take the screw out. The cover on the drain catches the screw before it falls into the drain. Twist the spout while pulling it straight out off the supply pipe. If there is not a set screw, it means there is an attachment between the supply pipe and spout.
Take a pipe wrench, grab the spout, and then turn it counterclockwise until the spout is removed. Take the spout to the hardware store, and get a new spout that attaches in the same manner. Use caution when choosing a new threaded spout because some connect near the outlet, but others connect near the base. The new spout must have the same connection as the old one. To install the new spout, simply reverse the steps it took to remove the old spout.