When I turn the hot water on/off in the shower it makes a very loud banging noise. How do I fix this?

Sounds like water hammer to me. Water hammer is usually recognized by a banging or thumping in water lines. The noise occurs when the flow of moving water is instantaneously stopped by a closing valve. This sudden stop results in a pressure spike behind the valve which acts like a tiny explosion inside the pipe. This pressure spike will reverberate throughout the plumbing system, rattling and shaking pipes, until it is absorbed.
Back in the 60's we were required to to put air chambers on all bath lavatories and kitchen sinks. Over time water and condensate built up in them and they must be recharged. First turn off the house at the main house shut off valve. Then open hot and cold faucets at the farthest bathroom to prevent air lock.(This is important.) You will find under each fixture little brass or chrome valves. These are called angle stops. With a small pail held under the angle stop to catch the run off look under the handle of the stop and you will see a nut with the stem running through it. This is called the bonnet packing nut. Put your wrench on it and back it off counterclockwise. Now open the stop and remove the stem and washer assembly, The stop will began to drain. When it has quit draining reassemble the stop and move on to the next one. Do this on each one of your angle stops. There will be six of them in a two bath home. When you are done, close off the faucets you have opened, turn on the water to the house, and give yourself a pat on the back.
You have just recharged your air chambers and saved yourself a hefty service call bill. Hope this helps you out and thank you for rating my reply. TOM

I had the same problem with my new house. The vibration of the hot water supply pipe from the hot water heater was the culprit. The first step I used was to turn all water off at the street, emptied the hot water heater and bled the lines. This was in case an object was causing the extra vibration. In the end, all I had to do was add an extra fastener to the pipe at the wall to secure from vibration and the sound went away. If yours is behind the wall, you may have to perform sheet rockery magic after securing the pipe. It was kind of fun to have the pipes wake up the family when I go to work early in the AM, but alas, my wife ensured I repaired the problem ASAP. Good luck.