First secure the plate by holding it firmly against your work surface. Next, slide the tines of the stopper tool between the top of the stopper strip backbone, keeping the underside of the stopper tool parallel with the top surface of the plate. Finally, lift the stopper tool vertically to remove the stopper gently. See a video of the technique here.
Do not use the stopper tool as a lever to pry the stoppers from the well, as doing so may cause displacement of the cells.