You should really avoid washing wood floors as much as possible. Find a good dust mop.

Years ago we used Fuller Brush mops with washable mop heads on all our wood floors.

I don't know the brand of mine but it has a microfiber pad at the end - I just dip the pad in a diluted solution, wring it out, then put it on the mop. MUCH easier than mopping with a bucket of water. The swiffer wet jet leaves my floors streaky.

I second the microfiber mop system. I have had several but my favorite came from Microfiber Tech on the web. (Look under "residential" when you go to microfibertech.com.) You can get pads designed for wet mopping and pads designed for dust mopping. The pads are washable and work great. This version of the mop is my favorite because it has a fairly large, flat mop surface and it has a low profile so I can get under my furniture easily (even under furniture that has very small space between the floor and the furniture bottom). The handle on this mop is very sturdy. I also have the Bona version of the mop which you can buy at Bed, Bath and Beyond. I think I also saw it at BJs or Costco too. It is just fine and easier to come by. The pads for these kinds of mops work on them all whether they were made for the Bona mop or the Orange Glo mop. (The Orange Glo mop is a disaster. The handle is so flimsy you can't put any pressure on it.) I also like the dust mop pads made by Casabella. They have a fringe around them. You can get them at Bed, Bath and Beyond. I use this mop on all my floors . . . tile, hardwood, vinyl. Works great.

This is what I use on my hardwood. I am not sure I would use Murphy's oil soap because it will leave a film if you don't wipe it dry. This system is easy. You spray the solution on the floor and then use the mop to get the dirt off. It dries streak free in seconds. No stickiness left at all. I have four dogs and this leaves my floors spotless.

Here is a link that might be useful: Mop

I have the Bona microfiber kit. I bought it directly online, but now I see that BB&Beyond has it, too (don't forget your 20% off coupon!).

I like the way it works. I always sweep the floor first (gets up people and dog hair and the little things that come in in your shoe treads and on puppy-dog paws). Then I spritz the microfiber pad quickly with the spray solution and do quick passes with it. I don't drench it.

This gives it a good, quick cleaning. Wood floors are resilient, so they don't need a lot of scrubbing effort. If I've spilled something, I use the Bona spray on a cloth and wipe it by hand.

When I had wood floors I used old washcloths, I dipped them in a solution of hot water with a little bit of dawn dishwashing liquid, rung them out real good then put the wash cloth on a swiffer, the kind you use the dry cloths on. This method worked great and left no streaks. .