Wiring it up isn't hard, IMO its best to forget you are wiring up a PLC and think of it as a light switch and a light bulb for a lamp.
In the case of your PLC OUTPUTS, your PLC is the switch. The "ACDC0" labeled terminal is one screw of your light switch, the "OUT0" is the other screw. So you take incoming power (in your case the 24+ of the DC power supply) and go to the incoming side of your switch (ACDC0). You then wire the power coming out of your switch (OUT0) to your light. The common on your light will go back to DC- on your power supply to complete the circuit. It is EXACTLY the same as wiring up a lamp in your house, except that instead of physically pressing a button to operate the switch, the PLC does it with software and you are using DC voltage instead of AC. Also, since you have relay outputs which behaves exactly like a mechanical light switch instead of transistors, the line voltage does not matter.
For your inputs, its the same analogy, but instead of your PLC being the switch, your PLC is the Lamp. You take incoming power (the hot leg of your AC) to one screw on your switch. You then take the outcoming power (the other screw on your switch) and go to the input screw on your LAMP/PLC. You have to complete the circuit, so your tie the neutral to the COMMON on your Lamp/PLC. This doesn't not work however if you use 24VDC power with a 120VAC light bulb, which is why voltage matters for your PLC inputs!