Hey Duke .... the diverter in tub spouts does corrode over time. Replacing it is relatively easy for a newbie.
Get a pipe wrench and remove the tub spout (turning it counter clockwise as you face it). The wrench will mess up the spout. Oh well. The spout is attached to a pipe stub (probably copper) which is threaded on the end. Clean the threads of the old putty or teflon tape.
Take the spout to your hardware store and get the closest match. You might have to buy a round eschutcheon which is a plate that sits against the shower wall to take up length. Get a roll of teflon tape ($1). Get a squeezable tube of kitchen/bath caulk (no gun required)
Here is where touch comes in ....Hand tighten the new spout just to see if you need the escutcheon. If you can reach the shower wall, then WHOOPEE. Apply teflon tape on the threads of the stub tightly, turning clockwise. Four turns of the teflon tape is usually adequate, making sure you work slightly down the stub (not all in the front, silly). Firmly tighten the spout until you are 3/8" from the shower wall. Put a rag on the new spout if you have to use the pipe wrench to prevent scratching the spout. Apply a bead of caulk to the wall-end of the spout before the final turns. Tighten as tight as seems good to get the right position for the spout.
If you need the escutcheon to fit tight to the shower wall, you can apply some caulk to the back rim of it. This will seal it to the wall, preventing water from getting behind it. Then apply the new tub spout until it is tight to the front face of the escutcheon.
Let the caulk cure overnight. Take a shower in the morning.