I have almost no water pressure on the cold water in my shower. It's an American Standard faucette that is at least 15 years old. It is the one handle style. What can I do?

Try this. Shut the water off and pull the cartridge, Check the inlet ports for trash and clean. Now place a pan over the open valve and turn the water back on for a minute to flush out the supply. You should have a strong stream when doing so. Reassemble and test. If that works do it on all affected taps, good luck, Tom