It's been well over twenty years since I last worked on a dental unit; but I doubt that the pneumatics (fluidics) side of things have changed that much.
If I remember rightly you could generally work things out just by opening the unit and looking ... at the tubing layout(s), and what-have-you.
In most cases you will be looking (or listening) for leaks, "loose" connections or blockages.
My advice is to get stuck in. Practice Makes Perfect, and all that stuff!
Hopefully you'll never have to deal with the Sterling Air Chair!