Most buy from overseas dealers in Israel, Belgium, India and Africa. There are many diamonds bought and sold in the major diamond "clubs" around the world and in jewelry centers like NYC, LA, etc.
You can be a dealer without overseas travel, too. You must pick a niche, invest a ton of money, service customers, finance their purchases and your own. You must also get to know how to make money and avoid costly mistakes. Mistakes happen in all business but the diamond business is a cruel teacher.