I understand that there is a lot to know about all the filters and other intricate parts of the circuit that fine tune the sounds coming out of the thing, but how does the basic circuitry work to create an output delay of the input signal?

 

It buffers and delays the input signal. It then lets you mix the delayed signal with the unmodified signal.
These are good resources:
https://www.electrosmash.com/pt2399-analysis
http://www.valvewizard.co.uk/PT2399_Data_Notes.pdf

 

Hello,

On ESP also a project is given:
https://sound-au.com/project26a.htm
Peter Vis also has some pages:
https://www.petervis.com/guitar-circuits/pt2399/overall-configuration.html

Bertus

 

Normally digital delays work by filling up a RAM from the ADC and then output these samples first in last out. In most digital delays the delay time gets set by memory allocation -the larger the RAM, the more time it takes to fill, so longer delay times.

In this particular IC though you vary the delay time by slowing or speeding the clock or rate at which the input is sampled. So it's a fixed memory size but filled up using different sample rates. Which explains why sound quality degrades quite a lot past 500ms, on the datasheet you can find a chart which shows the sample rate for each clock/external resistor value and correspondent delay time.