Clean the furniture with a tack cloth -- a sticky cloth that will pick up any tiny dust particles.
Brush the linseed oil solution onto the wood until it is covered evenly and allow it to sit for 30 minutes.
Fold the cheesecloth into a pad the size of your palm and firmly rub the oil into the wood, using a circular motion.
Wipe the wood with a clean cloth until only a thin film remains.
Allow the wood to dry completely. This may take up to a week or longer. You will know that the wood is dry when it is no longer sticky.
Reapply the linseed oil in the same manner as the first coat, at least 10 additional times, waiting until the wood is completely dry between applications.
Rub the wood with steel wool to achieve the degree of glossiness you desire. For a dull gloss, use 00 grade steel wool, and for a high gloss finish, use 00000 grade. Rub the steel wool along the wood's grain, applying light pressure, until the wood is uniformly glossy.
Dust the wood with a soft cloth.