An apparatus for use in cleaning a floor uses a flat mop including a generally flat mop head having a handle and absorbent fabric material. The mop head is foldable to a folded condition, wherein a loop of the fabric material depends from the folded parts. The fabric material is inserted into cleaning liquid to wet the material. The mop head is introduced to a wringer to wring the material between the jaws and a wringing surface. The damp absorbent fabric material is used to mop the floor. The floor is dried using a separate drying tool that includes a head secured to a handle, and one or more attachment devices to attach a dry absorbent cloth to the head. The floor is dried by applying the cloth to the floor using the tool and moving a dry portion of the cloth over the floor.