Once the tiles and grout look clean again, the real trick is keeping them that way for longer. After every shower, pull water off the walls with a squeegee or wipe the wettest areas with a towel. It takes less than a minute, but it stops moisture, soap residue, and minerals from drying into the grout lines again.
Ventilation matters too. Leave the bathroom door open when you can, run the fan after showering, and avoid letting damp towels sit against tiled walls. Grout loves trapped moisture, so anything that helps the room dry faster will make your next cleaning session easier.
When the grout is completely clean and dry, you can protect it with a grout sealer. Wait at least a full day after deep cleaning, then follow the instructions on the sealer you choose. This helps fill the tiny pores so dirt and moisture cannot settle in as quickly. It will not make your bathroom self-cleaning, but it gives you a much better head start. From there, a weekly wipe-down with warm water and mild soap is usually enough to keep the bright, fresh look going. It helps prevent dreaded grey lines from creeping back too quickly again.