see attached PDF - circled is the aircon clutch - the grey bit is the moving plate the gold bit is the pulley - there is a magnetic coil inside the clutch which pulls the plate towards rotating pulley and causes compressor to rotate. With the engine running and aircon off you can shine a torch down by the auxiliary drive belt and you will see the clutch plate is stationary even though the pulley is spinning around, now turn the aircon on and two things should happen, the radiator fans start up and the clutch should be energised and start to rotate with the pulley. there are also pressure switches on the system, a 'normal' pressure and a high pressure switch, if gas is low the low 'normal' pressure switch will not close, if the gas pressure is too high the high switch will tell the system, in either case the clutch will not pull in. There is also a high temperature cut-out on the side of the compressor, to stop it getting damaged and a 'low temp' (freeze warning) switch on the condenser (the cold radiator inside the car) - if either of these is activated the clutch will not pull in. The relay is in a small plastic box under the windscreen washer bottle filler tube MK2 ( box about 3 x 2 inches with two clips holding lid on ) and I think in under-bonnet fuse box on MK1 - it is about 20mm square with four spade connections underneath, the small spades are the coil and the larger pair are the main contact (about 40 amp rated) - if you can unplug the relay and put a voltmeter probe into the relay plugs, one of the larger ones should show 12volts and the other one of the pair you will need to switch to ohms and earth one of the probes and you should get about 4 ohms between relay contact and earth (the relay applies power to one side of clutch coil and the other side of clutch is earthed to engine).
As far as I know that relay is one of a pair of large relays, the other one is for heated rear window (but I don't think they are interchangeable).