Remove as much of the nonslip tape as possible. Pull it up by sliding the edge of a butter knife or an old credit card beneath the tape and scraping it gently from the wood.
Soak a clean rag with rubbing alcohol. Lay the rag over the adhesive and allow the alcohol to soak into the adhesive for three to five minutes.
Scrub the remaining adhesive from the wood with a clean cloth. Soak any stubborn spots with alcohol a second time, then scrub again.
Wash the area with a solvent-based liquid wax, formulated for wood flooring, following manufacturer's application instructions. The solvent wax breaks down any remaining residue and brings back the luster of the wood.
Buff the waxed area with a dry cloth until the excess wax is soaked up and all remaining dirt is removed.