Mop up excess water. Go over the entire floor with your mop. Work slowly to remove as much water as possible. Wring out your mop into the mop bucket periodically so that the mop is as absorbent as possible.
Dry any remaining standing moisture with clean, dry rags. Soak up the water, and wring out the rags into your mop bucket. Dry the floor as thoroughly as possible in this manner.
Open all the doors and windows in the room to obtain the best possible air flow. Place a fan in one corner or doorway that points into the room, and turn it on. Place the other fan in another doorway or corner that points out of the room, and turn it on as well.
Allow the fans to blow through the room for 12 hours to completely dry out your floor. Disconnect the fans, and remove them from the room.