Unzip the covers of the seat cushions and pull the covers off.
Slide the cover over a fresh foam pad. Either get one from the same store you got the recliner from or order one from a supplier. They cut the foam to match the specs of your old one.
Cut a small slit in the back of any cushioned areas that don't have zippers. Use scissors or a sharp knife to keep the cut as clean and straight as possible. Make the cut along a seam if possible.
Pull out the old foam through the incision. Go slowly to avoid making the cut wider than it has to be.
Stuff fresh foam into the incision once the old foam is removed. The foam could be from a furniture store, or you can get creative and fill it with stuffing from a pillow or comforter. You may need to glue foam pieces together with epoxy to provide thicker padding in the lower lumbar area, or else the chair may not be as comfortable.
Sew the incision shut with a sewing kit once that part of the chair has been filled with fresh material.