Let's use that mixer example from above. Suppose you can see that the limit switch is tripped, but there's no power coming out of the motor starter. Can you outline the next few troubleshooting steps?
The fact that the switch is in the tripped position means it is operating mechanically. But is it operating electrically?
Use the ladder diagram to determine the voltage in the switch circuit (e.g., 120V). Check for that voltage at the PLC input terminal corresponding to that switch. By checking here, you're using the "cut-in-half" principle of troubleshooting:
If the problem isn't on the input side, then use the ladder diagram to see what voltages should be present in the circuit that controls the valve motor. Experienced troubleshooters usually will begin at the most likely point of failure. In this case, that would be the thermal overloads on the motor starter.
The key to quickly troubleshooting a PLC-controlled system is to methodically check actual voltages against the expected ones, using the inputs and outputs of the ladder diagram as your guide.