grandkids, and 2,000 sq ft of oak flooring so I've had to really learn to clean them. Two 'bests' based on that level of need: 1) Warm water (20 oz), vinegar (5 oz), and rubbing alcohol (5 oz) mixed in a 32 oz spray bottle (EXAMPLE proportions). Spray this on lightly and use a hardwood floor mop to clean an area at a time.

Second method is to use a steam SHARK as it provides a deep cleaning steam to loosen the dirt with a soft cloth head to grab the dirt and wick it away. The head is washable and mine came with two, making it very convenient. Cost - around $50 at Bath, Bed, and Beyond - but look for a coupon and save $$$.

Good luck!