Hi, Gris. Most showers with 2 handles are simple compression types. They have a flat rubber washer that stops the water. The washers get old, hard, tired, abraded so you replace them. The problem is getting to the washer. There are a lot of different faucet designs available from many manufacturers. You normally have one nut to loosen that takes a special very deep socket. The special socket wrenches are available in many different sizes but they are only around $10 for a full set. Other than that, the only tools that you normally need are an adjustible wrench and a phillips screw driver.
You might look for handyman books or magazines that show pictures of the process. It is easy to do but hard to describe if you don't know the terminology. Don't forget to turn the water off to both faucets before you start.