Summarize this article:

Marble is very soft and prone to damage so it is important to apply a coat of high quality marble sealing agent before proceeding with the grout. This seal is also important because marble is very porous and grout can cause stains in the tiles.  Apply the sealing agent over the tops of the marble. Even if you prefer the color and look of unsealed marble you can use a “grout release”-type sealer to prevent grout from sticking to the marble tiles. Grout, or mortar, will be used ot fill in the spaces between the tiles. Be sure to wear a dust mask, safety goggles, and heavy-duty work gloves. Wear a long-sleeve shirt to avoid any possible damage to your skin from contact with the grout. Mix only enough as will be used in 15-20 minutes of work or else the extra can dry out and harden. This prepares the spaces for the grout or mortar. Spread the concrete evenly over the spaces between the tiles using a squeegee. Be careful to avoid getting cement on the tops of the tiles. Some will inevitably get on top of the tiles but you want to minimize the amount.  Try to push it into the spaces as much as possible to create a tight fight. Wipe up any grout on top of the tiles as you go. Use a squeegee to spread out the grout and leave a smooth surface in the cracks. You can also use a gloved finger to run down the grooves and smooth the top of the grout. Use a damp sponge to wipe down the tops of the tiles to remove any excess grout. Try not to get extra moisture into the grout or else it can make it too wet. Allow the grout to dry for the length of time required by the manufacturer. Some will require long curing times to ensure maximum strength. Use a disposable sponge applicator to paint the grout with a grout sealer. This will help prevent stains and dirt from permanently discoloring the grout. It will also make cleaning easier later on. Clean your tools with water or acetone to remove the excess grout or mortar and prepare them for use once again.

Summary:
Seal the marble. Mix grout according to the instructions on the packaging. Dampen the spaces between the tiles using a moist sponge. Fill the spaces with cement. Use a squeegee to spread out the grout. Use a clean sponge to wipe down the surface of the marble tiles. Allow the grout to dry. Seal the grout. Clean tools with water or acetone.