A clean hardwood floors makes a bigger difference than you'd think. Here's the most effective method, plus the mistakes most people make.
Remove all loose dirt, dust, and debris with a soft broom or vacuum on the hard floor setting (beater bar OFF).
Mix a small amount of Vibes Multi-Surface Cleaner in a bucket of warm water. The solution should be very diluted -- too much soap leaves a hazy film.
Dip the microfiber mop, wring it until barely damp, and mop in the direction of the wood grain. The mop should leave no visible moisture behind.
For polyurethane-finished floors, air drying is fine. For waxed or oil-finished floors, follow up with a dry microfiber cloth.