A good ceramic tile floor can be one of the most durable floor surfaces you can buy. Stains and spills are usually very easy to remove from the ceramic portion of the floor. The grout portion can be very different though.
For light surface stains on grout you can use an old school-style eraser and aggressively scrub the dirty section until the area is clean. You may also try lightly sandpapering the grout until the stain is gone. It is a good idea to vacuum up the residue as you go along to check your progress and to make sure you are not removing too much grout.
If those methods fail you should try one of the many over-the-counter grout cleaners available. Make sure to buy one without bleach or you run the risk of having lighter sections of grout which can make the rest of your grout appear dirty. Bleach will also make your grout become brittle much sooner and speed the need for you to replace it. Some of the “OXY” type cleaners do a real good job of cleaning grout stains without using bleach. Try using one of those and a soft plastic brush. That will take care of the majority of your stains.
After getting the grout clean sometimes it is a good idea to seal your grout. Sealers can prevent your grout from being stained for up to two or three years before having to be reapplied.
If the cleaning method dosen’t work for you it might be time to consider replacing the grout entirely.