Pull any remaining fragments of carpet tape slowly from the floor or other surface.
Apply 1 tbsp. of an adhesive dissolver or butane to a shop towel or rag. Wear a nose mask and latex gloves to keep from inhaling the adhesive dissolver or butane and to protect your hands.
Blot the two-way tape and residue with the rag or towel soaked in adhesive dissolver or butane. Do not rub -- this will lead to color transfer.
Reapply adhesive dissolver or butane to the towel or rag.
Continue blotting the tape and residue until it is gone.
If wet, dry the floor or other surface with paper towels.
Before installing another type of flooring, mop the floor with a damp mop or large towel, if possible.