I used a Porter-Cable 5/8” (the width of the staple top) Upholstery Stapler Model #US58, it’s the pneumatic model. Costs about $100 but I’m sure there’s cheaper ones available including some hand operated ones, which these are only good if you can get good steady pressure on a firm table/surface.
Make sure and measure thickness of both backer and material and use the proper sized staple, they come in varied lengths.