Note: This may be inacurrate, but it's what i've understood from my training so far.
There's a lot of phone calls. Firstly to agencies around the area where the aircraft is flying to try and work out if they're not working it. Usually in these instances in private pilots doing the flying, not big companies. If none of the local agencies are working it then call some of the other radar units to see if they are working it, or have previously worked it, or they know who he's possibly talking to now. A phone call to Distress and Diversion follows if nothing comes from the other units to see if they're working the plane as they may be lost. It's when you get the guys flying round with no radios that it gets interesting, and in that instance, you maybe get one of the other radar units to help you keep an eye on it to see if you can find out where it lands.
As Scuzi is actually a fully qualified Air Traffic Controller, and i'm still in training, he probably know the system a hell of a lot better than me, but that's how we work it at the college i'm at to give you a basic idea of the process.