Are you sure you know what you're getting yourself into here? 
To really understand what's going on, you'll probably need the equivalent of a bachelors degree in electrical engineering with an emphasis in digital signal processing. (Do you know the difference between "time domain" and "frequency domain"?) If that doesn't scare you off, I can suggest a couple books to get you started. My favorite introduction to DSP is:
Understanding Digital Signal Processing
by Richard Lyons
I also like:
Introduction to Signal Processing
by Sophocles Orfanidis
Chapter eight of the Orfanidis book goes into audio applications such as signal generation, effects like flanging, chorusing, echo, delay, compression, limiting, and some filtering to clean up signals.
As for what actually goes on in an Eventide box, I'm sure that's a company secret, one they don't want their competitors to figure out!
