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Start with a washcloth and some rubbing alcohol and gently wipe down where the scratches are. Take a cotton swab and go through each scratch with some rubbing alcohol to make sure they are cleaned out. Purchase a floor repair wax kit from your local hardware store (I recommend Picobello Flooring Repair Kit). Using the putty knife, apply wax to scratches and ensure its all the way inside the cracks. Once you are done, take the flat edge of knife and scrape off any excess wax. Last step just gently wipe repaired areas with a cloth to wipe up any residual wax.
For cleaning the floors, make sure you are using a damp (not soaking) mop with a small ammount of floor cleaner.
Hope that helps!
-Brittany