PID equations produce an analog output (CV, 0-100%)
If you have an On/Off device that you are trying to control with PID, you want to have the device ON for a fraction of a time-slice equal to the CV.
For example, you may have a time period of 60 seconds. If the CV is 50%, you would want to have the DO ON for 30 secs, then off for the remainder of the time. CV = 0 means that the DO doesn't come on, CV=100 means that the DO is ON all the time.
Tuning these kind of loops, then, is little different than tuning a regular analog loop, except that you mey need to play with the time period a bit to ensoure that you have a tunable loop. Too long, and the PID may alternate over/undershooting. Too short, and the DO may not have enough influence on the PV.
But once you get the time base about right (order of magnitude), do like you would with any closed loop: Set a manual CV and let the system stablize, change the CV and note the time lag between the SP change and the PV change, measure the slope of the PV change, etc., and get the tuning constants.
Whether you have integral or derivative will depend on the type of system.