Tell me a lot about your technical background so that I can coach you most effectively.
To trouble shoot the PLC you need a ladder logic diagram of the PLC programming and inputs. you can see what inputs are active or should be active, and if an input, such as a resistance read from a sensor is absent when you should be getting a resistance reading.. then you know that the problem is not in the PLC but in that particular input.
Most PLC's have many inputs and they vary in type from various DC voltage inputs, to switches, to voltage inputs of various sorts.
You verify the inputs first... If the inputs are all good and inputting as they should under the conditions, then you see if the outputs of the PLC are outputting as shown on the ladder logic diagram that defines what combination of inputs result in what combination of out puts, the outputs can be mere switches open or closed, or variable voltages for instance 0 to 10 VDC to input another device such as a variable speed pump or fan speed controller.
There can be various timers internal to the integrated circuit chip, or from various inputs that delay the action of an output... those are called I/O's input and outputs.
That is the gist of it. We can go from there, you will need a ladder logic diagram of how that particular PLC has been programmed.