Mix your cleaner in a sink or a small bucket. Use either a mixture of a very mild, noncitrus, dish detergent liquid and warm water, or use a neutral marble cleaner. You'll find the latter at most places that sell household cleaning supplies. If you use dish detergent, then 1 tbsp. per gallon of water should be sufficient.
Saturate a soft sponge in the cleaning mixture and scrub down the marble surfaces. For tougher areas of grime, you may need to add a little extra cleaner. For difficult-to-reach areas (high walls in/near the bath, for example) use a sponge mop instead of a sponge.
Rinse the marble with clean water. Dry it immediately with towels to avoid water spots. When you are drying, use a circular buffing motion--drying this way will make it appear more polished.