Sensors are easy.
Remember to only perform continuity or resistance (ohms) tests on components and sensors...NEVER on wires heading to the DME or cluster! Only test voltage on the DME wires. Unplug the DME to run continuity test on wires!
Crank position sensor - 680ohms(+/- 10%) between pins 1&2. Pin pairs 2&3 and 1&3 must be over 100Kohms. Sensor tip must be clean of oil residue and metallic debris, and must have an air gap between head and sending wheel not more than 1.3mm (roughly as thick as a credit card).
Cam position sensor - 1240ohms (+/-10%) between pins 1&2. Pin pairs 2&3 and 1&3 must be over 100Kohms
Coolant temp sensor (ETC) harness pin 1 (brown/red wire) must have 5VDC with ignition switch on. The sensor is variable resistance NTC; should be very high resistance if cold, dropping as the coolant warms up. BMW spec is 7-12Kohms at 14degF, 2-3Kohms at 70degF, 270-400 ohms at 180degF (operating temp). Be aware that there is also a gauge coolant temp sender in the E30. It has one pin on the sender. There is also an oil pressure sender plug in that harness...all three have the same style two-pin connector. Don't mix them up! E36 is similar, but it uses a dual-output engine temp sensor (ECT).
Airflow sensor (AFM) harness must have 5VDC between harness pin 1 and ground with ignition switched on. Pins 1&2 on the AFM will have a steady & variable resistance (ohms) as the door is moved through its travel. While you're there, test the intake air temp sensor (IAT). Pins 4&5 on the AFM should have 7-12Kohms resistance at 14degF, 2-3Kohms at 70degF. resistance will drop as the air temp gets higher.
Throttle position sensor is easy on the E30. With the ignition on, you'll need to have 5VDC between on pin 1 in the harness and ground. If the throttle is closed (idle position) you should see zero resistance (continuity) on sensor pins 1&2 and infinite resistance on pins 2&3. As you open the throttle plate, pins 1&2 must switch to infinite resistance. Move your DMM leads to pins 2&3. They must have infinite resistance until the throttle is almost fully open (WOT), at which point you'll see zero resistance. Be sure to test the TPS while it is installed on the TB - switch mis-adjustment, throttle cable too tight or a sticking throttle plate can prevent it from working properly. There are two slotted leads that permit limited adjustment of the TPS. I usually clean the TB with some alcohol/TB cleaner and a few shop cloths while I'm testing it out.
An E36 sensor is similar, but with a variable resistance. It'll also have 5VDC on harness pin 1. TPS pins 1&2 should increase resistance from 1-4Kohm as the throttle opens, pins 1&3 should read out approx. 4Kohms. Be aware that there is also a secondary TPS on E36 models with traction control...I'm not sure if the M42 models had this option or not.
The O2 sensor isn't easy to test properly. You can attempt to troubleshoot it with the following tests. The O2 sensor will output a rapidly fluctuating 0.2-0.8VDC signal when fully heated (>300degF) on pins 1&2 (be aware of dangerously hot components if attempting this test). Pins 3&4 on sensor harness (heater circuit) must have continuity. There must be battery voltage on pins 3&4 in the engine harness when the ignition switch is in position II.
Fuel pump must output 3.0 bar (43.5psi) +- 10%. The proper way to test the pump is with an inline tee fitting on the supply side of the fuel rail, or at the pump output under the rear seat. With the ignition on, you'll have to jump terminals 30 & 87 in the fuel pump relay socket to power up the pump. If you connect the pump directly to the testing gauge (known as 'dead-heading' the pump), you'll get an incorrect reading. A healthy pump can put out 80psi. Keep the gauge connected for at least 20 minutes; the system should lose no more than 0.5 bar (~7psi) pressure. If so, the pump's internal check valve is worn.
Ignition coils must have very low primary resistance - 0.4 to 0.8 ohms between the outer pins on E30 coils (Bosch calls them terminals 1&15). Similarly, the E36 quad-coil pack must read 0.4ohms to 0.8 ohms between the following pairs: 2&1, 2&6, 2&7, 2&5. Secondaries cannot be tested with a DMM.