Move the cabinet, once loaded, out from the wall as much as you can. Moving it will allow you to access the rear of the cabinet easily to see exactly where you will need to cut the holes. Unless the cabinet is extremely small, recruit an assistant to help you move it.
Use a pencil to mark on the rear of the cabinet the approximate locations of the audio components on each shelf of the unit. You can achieve this by eye or by using a tape measure. If using a tape measure, measure the height off the ground to the first component and then the distance from the edge of the cabinet to the device's plug.
Move all the audio components off the shelf to ensure they're safe from the cutting process. If the shelves slide outward, this movement might be enough to keep the components safe.
Drill a hole with a drill and a large drill bit if you wish to use a drill for this process to keep the holes small. Remember that each hole has to be big enough to allow not only the cord to pass, but also the plug. If you don't have a drill bit large enough for this task, you can use a jigsaw.
Cut a suitably sized hole in each designated area with a jigsaw. Cut each hole large enough for the plugs to pass through with ease.