Spray the grout lines with warm water, saturating the grout. Use a stiff bristled scrub brush to remove any light dirt deposits, scrubbing the surface of the grout in a circular motion. After scrubbing, rinse the grout with clean water.
Create a cleaning mixture consisting of equal parts vinegar and water. Spray the grout with the mixture, and allow it to sit for five minutes. Scrub the surface of the grout with a circular motion until the dirt or stain is removed, and then rinse the lines with clean water.
Make a cleaning paste by adding water to baking soda and mixing the two until the paste is the consistency of toothpaste. Spread the paste over the grout lines, and then spray the half-and-half vinegar and water solution over the paste. Allow the paste to stop foaming, and then scrub with a brush before rinsing the grout with clean water.
Remove any tough stains remaining after cleaning the grout by applying bleach to the stained area. Let the bleach sit in place for 10 to 15 minutes, and then rinse the grout with clean water.