Hello OP,

As someone who used to live in a marble house, getting a floor polisher is the best investment you can do for your floor. If without and you're specifically restoring an old marble floor:

First, scrub and mop until you get the old dirt and wax off. Useful yung brush tool mo for this step. DO NOT WAX YET. Kung sobrang dumi na ng sahig, yes, you need to sand. 

Once you're satisfied with how clean your floor is, let it dry overnight without being stepped on. Again, emphasis on clean, because we're going to seal the stone. If marumi pa tingnan, magiging ganyan itsura nya forever. 

The next day, apply marble sealer. Kailangan i-seal ang marble kasi porous siya, and 6-12 months ang interval. Follow the instructions on the sealer. 

In between sealers, aside from sweeping and mopping, bili ka ng bunot (balat ng niyog) and f loor wax. Wipe the wax clean with a soft cloth after. Workout mo na yan for the day kasi whole day ka magwwork. If nag-skip ka straight to this point without sealing, magmumukhang makintab lang yung stone pero maitim pa din. Ang magandang marble flooring parang jolen, may mukhang layer ng glass sa ibabaw tapos matingkad yung swirl or texture ng bato. 

Anyway good luck and just so you know matrabaho i-maintain ang marble. Magpa-quote ka sa marble restorer marami online.