Moisten the dried grout with a sponge and plain water. This will soften the grout a bit, making it easier to remove.
Scrape away as much of the grout as possible using solid oak sticks. You can buy these sticks at most home improvement stores, or craft them yourself. Don't scrape off the grout with metal, as this may scratch the tile surface. Remove the grout that you were able to remove, with a broom or vacuum cleaner.
Dip a few cotton balls in nail varnish remover and rub it over the remaining grout on the tile. This will remove any grout that is still stuck to the tile
Wash down the area with warm, soapy water and a sponge. Polish the tile with a soft, dry cloth.
Use a nylon scouring pad to remove the grout haze that may be left on the tile. Use a generous amount of plain water and scrub the tile with the nylon scouring pad. Use a soft, dry cloth to soak up the excess moisture.
Allow the tile to dry completely. Inspect the surface for traces of old grout or grout haze. If there is still grout residue on the tile, then repeat Step 5 until all of the grout and grout haze have been removed.