Purchase grout in the same color--or as close as possible to the same color--as the grout you're about to repair. Most grouts are white or off-white.
Mix the grout with enough water to form a wet paste. A slightly runny texture ensures the new grout is able to get into the crack and not just on top of it.
Apply new grout to the cracked area, using your finger or a small sponge to press the grout into the crack.
Wipe away excess grout from the tiles after it has set but before it dries, using a damp sponge. Leave the tiles to dry completely.
Buff the surrounding tile with a soft, dry fabric such as cheesecloth to remove any grout haze that remains. Allow the grout to dry completely.
Seal the patched area with a standard grout sealer.
Remove all loose material from the cracked area, using a carbide grout scraper or a flat-head screwdriver.
Widen the crack slightly, using the screwdriver. This provides the new grout with a surface it can better adhere to.
Mix the new grout into a wet paste and apply to the crack with the sponge.
Wipe away excess grout after it has set but before it dries, using a damp sponge.
Buff the surrounding tile with a dry, soft fabric cloth to remove any remaining grout haze. Let the grout dry completely and seal the patched area with a standard grout sealer.