* A code reader: This is the easiest and most reliable method. A generic OBD-I code reader (since it's a pre-OBD-II vehicle) will plug into the car's diagnostic port (usually under the dash) and display the trouble codes.
* A multimeter: You can use a multimeter to check for voltage at the diagnostic connector pins to interpret flashing lights or voltage changes which represent the codes, but this requires a deeper understanding of the vehicle's diagnostic system and is more time consuming. There are specific instructions for this process, often available in repair manuals specific to the 1992 Ford Tempo.
The key cycling method you're referring to was a feature of some earlier GM vehicles, but it wasn't used by Ford in the 1992 Tempo.