Sweep

The World Floor Covering Association recommends sweeping your ceramic floor, especially those with texture, to loosen and remove large particles and most dirt.

Mop

Most dirty ceramic tile floors will clean up well with a damp mop and a mild cleaning solution.

Oxygen Bleach

For stubborn grout stains, use oxygen bleach. According to AsktheBuilder.com, apply a solution made by stirring together oxygen bleach and warm water (follow the bleach manufacturer's instructions) and let it soak into the grout for a half-hour to an hour. Leave a standing layer on the grout. Scrub, mop and rinse.

Hydrogen Peroxide

For a cheap solution to moldy grout, try hydrogen peroxide. According to HowtoCleanStuff.net, pour ½ cup of hydrogen peroxide into a spray bottle with 1 cup of water. Spray the solution on the grout to clean already dirty grout or as a preventive measure.

Acid

As a last resort for particularly nasty grout stains, consider phosphoric or muriatic acid. According to NaturalHandyman.com, purchase either acid at your local hardware store, and follow the manufacturer's directions and cautions to the letter. Acids can cause serious injury.

Source:

World Floor Covering Assocation: Ceramic/Porcelain Care

AsktheBuilder.com: How to Clean Grout

NaturalHandyman.com: Muriatic Acid and Cleaning Masonry Surfaces