White vinegar (never, ever cider vinegar) diluted with very warm water, plus elbow grease.
Swiffer wet pads (NOT the "wet jet" swiffer which was lousy) are fine in between vinegar and water cleanings. I have never used a steamer, but if you do call the maker and get them to assure you it's OK for hardwood. If your hardwood is older, it may not have a finish designed to stand up to regular steaming -- wood hates moisture, so check it out first.
If you mop, use a dry mop afterward! Like I said - wood hates moisture. I always dry the floors after washing! It only takes moments but will help preserve them.
Hardwood is far better than carpet -- carpet traps and holds so much dirt, allergens, etc. Gross. I feel I can get hardwood cleaner much more easily, and I can see small items on the floor that would get buried in carpet.