Attach washers to as many long screws as you need to attach the cabinets to the wall. Spin toggle bolts onto the screws after tightening the washers.
Drill pilot holes in the area of the wall where the corners of the cabinets will be. Drill holes in the back of the cabinets so that they line up with the holes in the wall.
Lift a cabinet up to the wall. Insert screws with toggle bolts through the holes in the cabinets and the wall. Push the bolt through until its spring-loaded wings expand on the other side of the wall.
Tighten the screw until the washer rests firmly against the back of the cabinet. Insert and tighten screws in the other holes until the cabinet is secure.