IMHO regulators are required, but if you have the little blue compressor Testor sells it barely puts out enough air to begin with. You might want to save up some money and buy a more robust compressor before you get the regulator!
Regulators are just taps for air. The gauge assists you in dialing the proper pressure for painting. Too little and the paint doesn't atomize, too much and the paint dries before it gets to the model.
Pressure regulators run the gamut from expensive to cheap. "Proper" airbrushing regulators show a scale that is from 0-30 psi or 0-50 psi and are IMHO expensive. I use a cheap (under $10) regulator like this one that comes from Harbor Freight. The scale goes up to 160 psi, but I use only a small portion of it for airbrushing.
Typically they use 1/4" NPT threads. Mine came with two "female" connections, which allowed me to connect my compressor hose to the inlet side, but I needed a "male to male" connector to attach my airbrush hose to the outlet side. The one pictured at HF looks to have the right connectors out of the box.
This one comes with both moisture trap and regulator, and requires the connectors I mentioned above. It's a pretty good deal, but where would you mount it on your compressor?