Here are a couple of resources that will help you learn about antenna tuners. The first was posted by Richards, K8JHR, to the HamRadioHelpGroup mailing list. It is a presentation on antenna tuners given by W0QE, who was involved in the development of Palstar’s new HF-AUTO tuner. There’s lot of good info, but it’s missing the context that the talk would have given.
The second is an online antenna tuner simulator that appeared in the September QST. By playing with it, you can see how changing the settings of the tuner affect the values of the capacitors and inductor and how eventually you get to a matching condition.
It would be interesting to have such simulators for various other matching networks, such as the L-network for matching random wires and for the matching network used to match end-fed, half-wave antennas.