Can anyone give me a brief overview or links to articles that might explain how different components might affect a sound signal?
Instead of messing about with components, the modern way to modify sounds is in the digital domain, with digital signal processing (DSP). The audio is digitised by sampling with an ADC, modified with software running on a PC or DSP chip, and then converted back to analogue using a DAC. The ADC and DAC are usually combined in a codec chip.

An ideal device for experimenting with this technique is one of the Microchip 16-bit dsPICs. A few years ago I designed this low-cost audio processor based on one. It was intended for speech processing for amateur radio, but it would work equally well for guitar effects. PCB Gerber and drill files are available here, in the Files section. You need to join the group to access them.