Turn on a hair dryer and move the warm air coming from it over the fuzzy surface to melt the wax, polish or oil that holds the fuzz to the table's surface. Continue to warm the surface until the tabletop feels tacky.
Rub a lint-free cloth vigorously over the fuzz. Begin at the edges of the fuzz and work toward the middle of the patch. Continue to warm the fuzzy area and rub with a lint-free cloth until no fuzz remains on the table. If the fuzz remains, move to step 3.
Soak a lint-free rag into mineral spirits. Rub the fuzzy section, beginning at the outer edges, working toward the middle to pull the fuzz from the table. Turn the rag often to avoid redistributing fuzz on the table. Continue to rub the fuzz patch until the fuzz is no longer visible.
Add 1 tsp. of mild dish soap to 4 cups of water. Dip the end of a lint-free rag into the soapy water. Wipe the surface of the table to remove the mineral spirits residue. Dry the table with a lint-free rag.
Apply a coat of polish, wax or boiled linseed oil, depending on the original finish, with a lint-free rag on the table to protect the wood finish.