Mix 1 gallon of water with 1 cup of white vinegar. The white vinegar will help remove hard water and soap residue stains.
Dip a mop into the solution, and wring it out as much as possible so the floor is just slightly damp. Don't soak stained wood floor, as this will damage it.
Push the mop over a small area on the floor. Push along the wood grain until the floor appears shiny.
Rinse the mop with clean water, wring it out, and then apply more cleaning solution. Repeat the process until the entire floor is clean and doesn't have any residue on it.
Dry the floor immediately with a terry cloth towel, and push it along the wood grain to shine it. Oftentimes, this is all you need to do to shine a stained floor.
Buff a small area of the floor with a microfiber cloth. Buff along the grain using pressure until it appears shiny and smooth. Repeat the process on the rest of the floor.