They're neat little devices...but pretty simple actually.
The first thing I do when I get a used regulator is to hook it to a CO2 Tank...back the set screw off all the way...and open the tank valve.
With a little soap solution...go around the HIGH PRESSURE port connections (3 o'clock, and 9 o'clock position... look for little bubbles.
Next with the soap solution...check the weep hole. Or better yet with a Cornelius regulator...just remove the 4 screws holding the cover on..and put the soap solution directly on the poppet valve--- and also around the seam between the Stainless Steel Valve Seat and the machined brass body. There's a thin gasket in there that leaks sometime. So, there should be no bubbles. If there's leaking around the poppet valve...you may need a rebuild kit to replace that. If the valve seat peice leaks...you'll have to press it out and seal it with a thin film of RTV sealant. Press it back into place while it's still wet. Let it dry and clean up any excess. (note: some manufactures have threaded seats...don't try to press these out)
That's where most of the leaks come from.
If no leak there...reassemble the Diaphram, needle valve, spring, cover...and adjust the screw to set the pressure. With it stable...check the weep hole again. If it's bubbling...your needle valve isn't seating or the diaphram has a hole in it...either way, they're parts included in the rebuild kit.
Finally, check the fittings for the Low Pressure Gauge, and the outlet port. 12 o'clock and 6 o'clock.
Pay attention to the High Pressure ports on Primary regulators. They're usually Left Hand Thread. Secondary Regulators are usually Right Hand Thread.
Not much to them.
Hope that helps with troubleshooting a regulator