A lot of it involves complex math, but musicdsp is a good place for code snippets. Airwindows also has his source code on his github. Forums like the JUCE one are also helpful, or just google searching specific topics like "saturation DSP C++" or "non-linear DSP", something like that.
Basically we take the samples in the buffer and do some sort of math to them to change how they sound, this ranges from simple multiplication (gain/compression), waveshaping (saturation), to more complicated things like pitch-shifting or FFTs.
It's a big topic.