There are many different ways to attach a shelf to a drywall you will need to pick which method is appropriate for the weight of the shelf and what is going to be stored on it. If the shelf that you are going to hang it going to be light then plastic anchors will be fine, the plastic auger is like a screw and will attach into a pre- drilled hole and sit flush with the wall acting as an anchor.
You will need to make sure that the holes you drill are level. It is advisable to drill a pilot hole so that the drywall isn’t damaged when you screw the auger in place. Once you have done this for all the holes, line up the mounting bracket and attach a screw through each of the holes into the plastic anchors then simply tighten the screws and put the shelf onto the bracket.