Car wax. Something with carnauba wax seems to be the recommended as being the best. As long as you have no grout for it to get into, it should bring back the shine, and provide a protectant against staining. The sites I've found recommend doing it about 2-3 times a year.
I did this with a all-in-one sink vanity top that was older than dirt (eventually hope to replace), and it looked pretty good. Just don't get it into grout or tight seams or have a soft toothbrush handy to scrub it out (and try to avoid the ones with a color additive if so - the color stains grout slightly)
I'd do a spot test first, but I was personally happy with it.