If you've ever wiped dirty fingerprints off a latex painted wall, you will know that the paint removes almost as easily as the finger smudges. Knowing this can make you a little reluctant to clean the painted wood floor in your house, but if you take the proper steps, you can end up with a clean and still painted floor.
Hopefully you are working on a floor that has been painted with a high gloss, oil-based latex enamel paint. This is the best scenario because this type of paint is a little more durable and water resistant than water based semi-gloss, satin, or flat paint. You still can't flood-mop it like you might do to a linoleum floor, but it buys you a little more time. If you are working with a more sensitive paint you may want to consult a cleaning professional or your local hardware store's paint clerk before your proceed.
Start by filling a mop bucket with water and a measure of vinegar; a little bit of vinegar goes a long way, so you probably don't need more than a fourth cup for most mop buckets. Dip your mop in the vinegar solution, and ring it out as dry as you can. The mop should be damp, but not drippy. As always, start in a corner and work your way out.
It's important that water doesn't sit for very long on the surface of the paint, because water will seep through even the glossiest of enamels if left for more than a few minutes. You may want to consider working in small sections, and dry one section before you mop the next. There are several ways to pick up moisture that your mop has left behind. A dry mop, reserved for this purpose, works really well, but if you don't have an extra mop lying around, then you can use an old towel or a paper towel. If you are using some type of towel, wipe lightly. Don't rub, as that will remove paint. Also, avoid walking on damp sections, as doing so may peel up paint or leave an indent on the softened surfaces. Make sure the floor is completely dry before you allow traffic.
Over time, paint loses its elasticity, and if you notice some cracking on your floor, you may want to spot treat with a small amount of olive oil. Any type of olive oil will work for this, so you may want to save the expensive extra virgin import and opt for a lower grade olive oil if you have it on hand. Pour a small amount on the rag (you won't need much, the spot on the rag should be about the size of a finger print) and gently rub it into the distressed spot.