Examine the exposed wood details carefully. Wood added as decoration has a flat back. You can also slide a flat spatula or the dull side of a knife between the decoration and upholstery.
Sand the exposed detail smooth if the wood is part of the frame. You can add padding over it, if necessary when you reupholster. Before cutting off or sanding the detail on an old sofa, though, have the piece evaluated. You may be able to get enough money for it to replace it with exactly the new piece you want.
Remove any hardware or metal decorations that cover corners or the ends of wood piecework decoration.
Carefully pry up the wood decorations. Use a tack puller or claw foot hammer to gently raise the wood and remove each piece separately. Slowly separate glued wood with a chisel and mallet.
Clean up the underlying frame before recovering the area. Pull protruding tacks, nails or screws and sand splintery edges.