With access to a pottery studio, it would be fairly easy to make something that looks like that; however, it might take some effort to find the exact pigments the Greeks used, and it would probably be a hassle to build a pottery wheel like the ones used in ancient Greece. If you want to be authentic without spending lots of money and effort, you would probably use a non-electric wheel, and look for modern clay pigments/glazes that incorporate some of the same pigments the Greeks would have used. The Met has an essay on the techniques that you're asking about.