To replace bathroom grout, first use a rotary tool that is fitted with a grout-removal attachment to remove the existing grout. Vacuum the area to remove the dust, and apply new grout that is mixed with a latex additive, using a grout float. Wipe the excess grout off the tile using a damp sponge, and buff the tile with a dry cloth. After one week, apply grout sealant to the new grout.
If a rotary tool or the appropriate attachment isn't available, remove the old grout with a grout saw. Mix the grout according to the directions on the product packaging, and apply the grout and latex mixture by loading the float with the grout mixture and making diagonal sweeps across the tile. Continue applying the grout until the tile seams are filled in.
After applying the grout, wait 20 minutes, or until a white film appears on the tile, before wiping the tile with a damp sponge. Rinse the sponge frequently during the cleaning process, and allow the tile to develop a second white film before buffing it with a dry cloth. Apply a grout sealer according to the directions on the product label after the grout has cured for the recommended amount of time.