Mix a loose solution of dry, non-sanded grout mix and water, or add a little water to a small amount of non-sanded pre-mixed grout. You will only need a tablespoon or so of the grout solution.
Spray the grout lines with water and wipe away any excess.
Dribble the thinned grout, using a spoon, over the hairline cracks. The grout should be thin enough to enter the crack. If it is not, thin it out a little more by adding more water.
Push the grout into the hairline cracks by working it with your finger. When the cracks are filled, wipe off any excess grout from the tiles and let the grout line dry.
Check the grout line after it has dried. If the new grout has shrunk upon drying, and the hairline crack is still visible, repeat the process of applying thinned grout to the hairline crack until the crack is no longer visible. Allow the new grout to cure for 48 hours.
Polish the tiles and remove any remaining grout haze by buffing the tiles with an old T-shirt.
Remove as much cracked grout as possible by hand. Use a stiff metal brush to help remove the grout and clean the joint.
Mask off the tiles along the edges of the cracked grout. This helps prevent scratching the tiles as you are working on the grout line.
Put on the safety glasses. Use either a hand-held grout removal tool or a specialty grout-removal power tool to remove the cracked grout. Remove 2/3 of the depth of the grout, leaving the remaining grout in place only if it is firmly attached to the substrate.
Vacuum the area to clean it of grout dust and debris.
Remove the masking tape from the tiles. Spray the grout lines with water and wipe down the area with a sponge.
Pour the dry grout mix into a bucket and add water according to the package's directions. Let the grout mixture rest for 10 minutes. You can use sanded grout mix on wide grout lines, but do not use sanded grout if you have marble tiles.
Scoop up some of the grout mixture with the grout float and press it into the grout lines, working diagonally across the grout lines.
Dampen a grout sponge and wipe off any excess grout from the tiles, using light strokes across the tiles and grout lines to avoid removing the wet grout from the lines. Rinse the sponge often in a separate bucket of water.
Allow the new grout to cure for 48 hours, and then polish the tiles and remove the grout haze with an old T-shirt.