Using the PC817 IC is pretty much straightforward, we just have to connect the anode pin of the IR LED (pin 1) to the logic input which has to be isolated and the cathode (pin 2) of the IR led to the ground. Then Pull high the collector pin of the transistor using a resistor (here I have used 1K) and connect the collector pin to the output of your desired logic circuit. The Emitter (pin 4) is grounded.

Note: The ground line of the IR LED (pin 2) and the ground line of the transistor (pin 4) will not be connected together. This is where the isolation occurs.

Now, when the Logic input is low the IR LED will not conduct and hence the transistor will also be in an off state. Hence the Logic output will remain high, this high voltage can be set anywhere up to 30V (Collector-Emitter Voltage) here I have used +5V. Their pull-up resistor 1K acts as a load resistor.

But when the Logic input is made high, this high voltage should be a minimum of 1.25V (Diode Forward voltage) the IR LED conducts and so the photo-transistor is also turned on. This will short the collector and emitter and hence the Logic Output voltage will become zero. This way the logic input will be reflected in the logic output and still provides isolation between the two. The complete work can also be understood from the GIF file above.

Another important parameter to consider while using an Optocoupler is the rise time (tr) and fall time (tf). The output will not get high as soon as the input logic is made low and vice versa. The below waveform shows the time taken for the output to transit from one state to another. For PC817 the rise time (TPDHL) and fall time (TPDLH) are 18us.