Is your grout really dirty looking and stained? Try a little bit of Baking soda and water. Make a loose paste and spread over the grout. If its a tough job let it sit for 30 minutes. Gently scrub with a 1/2 ” brass brush. If you’re worried about scratching your tile you can try a stiff nylon brush. If the stains are stubborn try pouring a wee bit of hydrogen peroxide over the paste. When the fizzing stops go ahead and lightly scrub. This should bring your grout back to the color it was when you first grouted. Please test this out in an inconspicuous area before going ahead with the rest of the floor. Wipe up the baking soda with a clean sponge rinsing thoroughly as you go. When you’re all finished mopping and drying the floor you may also want to treat the grout with a grout sealer.
Its always wise to check with the manufacturer or your tile setter before doing anything to your floors.