Remove any paint drips or spatters from the tile as soon as possible. Paint takes about a week to completely cure, so you may be able to use a fingernail or plastic putty knife to work the paint drips free. If you're concerned about scratching the tile, wrap the end of the putty knife in a rag.
Apply warm water to latex paint drips and keep the paint moist. This allows for easy removal with a rag or putty knife. Wipe with a rag to remove completely. If paint drips onto the grout, let the paint dry completely for at least a week. Mix water and a small amount of light detergent and apply the solution to the grout. Scrub the grout clean with a scrub brush or slightly abrasive scrub pad.
Remove old paint by wetting the tile with isopropyl alcohol and covering the tile with plastic to prevent evaporation (make sure the tile is damp). The alcohol will soften the latex paint and allow easy removal with water and detergent. This method works well for larger tile-restoration jobs.
Remove oil-based paints from tile by applying turpentine to a rag and gently rubbing the tile surface. Turpentine is a solvent and should be used only with proper ventilation. Nail-polish remover is a gentler version of acetone, a product that can also be used to strip paint from tile without damaging the glazed surface of the tile.