Start with the easiest step first: plain warm water and a firm little brush. It sounds almost too simple, but this first pass matters. Wet the tiles and grout, then scrub along the lines in small circles. You are not trying to win the whole battle yet. You are removing loose dirt, old soap residue, and the thin surface layer that blocks stronger cleaning from reaching the grout.
Use a brush that is stiff enough to work into the lines, but not so rough that it scratches the tile or chews up crumbling grout. An old toothbrush can work well on small areas, while a narrow grout brush is better for a larger floor or shower wall. Work in sections so the surface stays wet while you scrub.
After scrubbing, wipe everything with a clean, damp cloth or sponge. This shows you what is actually stained and what was only sitting on the surface. If the grout already looks brighter, stop there and rinse well. If the dark lines are still there, you have prepared the area properly for the next step, which is where the deeper cleaning begins. This saves effort and helps your cleaner work more evenly, too.