When discolouration occurs, particularly in the grouting, it is advised that the areas are treated with a stronger cleaner like bleach. A scouring pad or scrubbing brush may be necessary to fully clean the grouting or between the cracks in the tiles, but ultimately it depends on how deep you want the cleaning.
Superficially a mop is enough. It follows the same basic premise as most mopping: overlapping strokes in a consistent direction slowly covering the area. A cleaner with a disinfectant is a must for these areas, particularly considering the room likely has a toilet in it.