Welcome to the daily halacha (Jewish law). On Shabbat, the Shulchan Aruch writes that a person cannot wash the floors. If you have a marble floor or a wooden floor, you are not allowed to wash it on Shabbat. Why? Because we're afraid a person is going to do sechita; that's asur (forbidden). What is sechita? Sechita is whatever towel you're using, or whatever sponge they're using to clean the floor, or sponge as they call it in Hebrew. We're afraid they're going to squeeze liquids—that is, squeeze water out of it—and that's asur on Shabbat while you're cleaning the floor.
If a big mess spills on the floor—let's say a bottle of Coke spills—you could take a very, very thick towel. Try to take a colored towel, not a white one; take a black one, a brown one, a dark blue one, a dark purple one, whatever it is, but just not a white one. Then you can wipe off the Coke from the floor, but be careful not to squeeze the Coke that got absorbed inside the towel, because that will be asur on Shabbat. If you have to use a futon, then use a few towels, but actually squeezing out the towel you used to clean up the Coke that spilled on the floor will be asur. If you have tissues, that's better. It is better to use paper towels and tissues to clean the Coke that spilled on the floor than to use a towel. But if you're going to use a towel, make sure it's a very thick towel that can absorb a lot, and, two, make sure it's a colored towel, not a white one.
Another reason why you're not allowed to wash the floors on Shabbat is that the Hachamim (Sages) had a special gezerah (a special decree) that a person should not sweep his floors on Shabbat, a person should not clean his floor on Shabbat. But in our day, Hacham Ovadia Yosef says that sweeping the floor with a broom is halachically fine. You're not allowed to sweep outside your house. Let's say a person wants to sweep his driveway or his path toward his house. Outside your house, a person should not sweep, even cement floors. But inside the house, you can sweep.
But cleaning the floor with water is still asur on Shabbat. Hacham Ovadia Yosef does say that if you have something that fell on the floor, just a small amount of dirt, or something that got glued to the floor, you can, if you want, spill a little water on it and then clean it with a very, very thick towel. But actually starting to clean the floors and use sponges—they say, starting to mop the floors on Shabbat—is something you're not allowed to do.