Examine the arms of your couch to determine where the ends of the upholstery are hidden. Some sofa arms have a separate padded front panel to hide seams, while others have staples under the bottom inside lip, next to the cushions. Still others have separate covers for the arms that are sewn as one piece, slipped on and stapled at the bottom of the structure.
Uncover the arms to expose the top and inside. Use a thick, flat-head screwdriver to pry staples out, or use a seam ripper to pluck out stitches. It's not necessary to separate the cover from the structure entirely, as long as the arm is exposed from where it meets the cushion platform to just under the top roll on the outside.
Remove the existing batting. In most cases, it is attached with a light adhesive and should peel off pretty cleanly, but sometimes it's sewn on at either end. Use scissors to cut it loose if you must -- it's okay to leave a few traces of it if some parts are difficult to remove.
Measure from the inside base of the arm, over the top roll, to under the roll on the outside of the arm. Cut a piece of new batting to that length.
Apply spray adhesive to the new batting and smooth it into place. If your batting is narrow, you may need two pieces to cover the arm. Apply the front piece first, then butt the rear piece firmly up against it and spread the top layers of the two pieces to hide the separation.
Apply another layer of batting if desired, but don't try to make the arm more padded than it was originally. Keep in mind that the original cover still has to fit.
Replace the arm cover. Pull it tight over the arm, and reattach it to the sofa the same way it was attached originally. If your cover was sewn on and you're no good with a needle, use a staple gun with upholstery staples to tack it back on. Whatever method you use, be sure to pull the fabric evenly taut. Periodically check the overall look of the arm for fabric distortions that could indicate a too-tight or too-loose pull in one area or another.