For grout that still looks dull, make a thick paste with two parts baking soda and one part hydrogen peroxide. Add a few drops of mild dish soap if the tiles have greasy residue or that slippery bathroom film. Stir until the mixture is creamy enough to stay on the grout instead of running down the wall or disappearing across the floor.
Spread the paste directly over the grout lines with a brush, sponge, or gloved finger. Do not rush into scrubbing immediately. Let it sit for about ten to fifteen minutes so it can soften the build-up inside the tiny pores. This waiting time is what makes the job feel much easier later.
Now scrub the lines gently but firmly. Move with the grout, not just across it, and pay extra attention to corners where moisture tends to collect. When the lines begin to brighten, rinse the area with warm water and wipe away every bit of paste. Leftover residue can dry into a chalky film, so go over the tiles once more with a clean, damp cloth. Then dry the surface and check your progress. Good rinsing is just as important as the scrubbing itself here every time.