overdrive op amp
The circuitry that Audioguru describes is the most basic type of overdrive type distortion and could be described as fuzz.
A lot will depend on the exact type of overdrive that you want . If it is the type of overdrive that you get with a amp bring driven to its maximum and then distorting well this can be quite dificult.
It can only be done by actually using a amp and speakers being overdriven and ecoustically ballanced and then re miced up.
All sorts of things come into play, phase shift, attenuation, speaker distortion sustain, etc.