Here's a list of things to check and how to check them.
1. A/C clutch coil itself. You can use a voltmeter across the two terminals on the compressor connector. Should not be open. As an alternative, connect +12v to one of the pins, ground the other and see if the compressor clutch "snaps closed". If so, the clutch is good.
2. high-pressure cutoff switch is near the radiator on left side. It has 4 pins, two for the clutch, two for the fan. Chilton's gives the color coding. Jumper across the two compressor pins. If the compressor comes on, the high-pressure cutoff switch needs to be replaced.
3. If that fails, check the pressure cycling switch, on the accumulator/drier over on the passenger's side next to the firewall. Disconnect the connector and jumper between the two pins. If the clutch engages, replace the switch.
4. If that fails, check the same connector to see if you get +12 volts between one of the pins and ground (test both, one should be +12). If so, then the most likely candidate is the CCRM which is inside the passenger's side fenderwell. It is a 150 buck box that contains the A/C relay, fan relay, fuel pump relay, etc. But you have to replace it as a unit. If you don't get 12 volts across the cycling switch, you probably are left with a blown fuse or a switch problem in the dash.
The circuit is pretty simple. +12 comes from the A/C switch on the dash, and goes in series thru the cycling switch, the high-pressure cutoff switch, and to the relay in the CCRM before arriving at the clutch coil. If any of those are bad, no A/C. If the clutch coil goes out, it can burn the relay in the CCRM, which means replacement.
All of this assumes a good charge, somewhere between 70 and 120 psi with the motor turned off, measured on either line since they should be equalized. Cool morning = 70psi with a normal charge. Hot at noon can go to 120psi or so. Low pressure (well below 70) will prevent it from coming on... So you need a good R134a charge before testing anything else.
It is a simple system, and with a good chiltons/haynes book to give you the color coding, it is not hard to follow the wiring, and find/fix the bad component.