Here's my tip for the quickest way to cover matboard with paper- spray adhesive.
Cut a sheet of 12" x 12" paper in half. Lay it face down in a well ventilated area or inside a spray box. Coat the wrong sides of the paper with spray adhesive. Position the paper on top of a piece of matboard and press in place. The pressure of running it through the die cut machine fuses the paper and matboard together. So cool!
Paper may be added to both sides of the matboard if desired. Sometimes when I add two pieces of thick cardstock, the score lines are a little stiff since this is a bit thicker than what the die was designed to score. Just take your craft knife and trace over the scoring lines with light pressure. That should make the matboard easier to bend. Then fold each score line over 180 degrees. This breaks the paper fibers and makes it easier to work with.