To remove stains and old dirt on ceramic and tile floors, you can follow these steps:

1. Start by sweeping or vacuuming the floor to remove loose dirt and debris.
2. Mix a cleaning solution by combining equal parts of vinegar and water. Vinegar is a natural and effective cleaner that can break down stains and dirt.
3. Apply the cleaning solution to the stained areas on the floor. You can use a spray bottle or a mop soaked in the solution.
4. Let the solution sit on the stains for a few minutes to allow it to penetrate and loosen the dirt.
5. Scrub the stained areas using a soft-bristle brush or a scrub brush. Make sure to scrub gently to avoid damaging the surface of the ceramic or tile.
6. Rinse the floor with clean water to remove the cleaning solution and any remaining dirt.
7. If the stains are stubborn and don't come off with vinegar and water, you can try using a commercial tile and grout cleaner. Follow the instructions on the cleaner's packaging for best results.
8. After cleaning, dry the floor thoroughly with a clean towel or allow it to air dry.

It's important to note that some stains may require additional treatment or professional assistance. If you're unsure about how to remove a specific stain or if the stain persists after cleaning, it's recommended to consult a professional.

References:

• The Spruce - How to Clean Ceramic Tile Floors
• Bob Vila - How to Clean Tile Floors