There are two distinct sections of the market as a whole. The "outer market," known as jōgai-shijō, is a mixture of wholesale and retail shops that sell Japanese kitchen tools, restaurant supplies, groceries, and seafood, and many restaurants, especially sushi restaurants. The main market area is open at 9:00am to tourists (most of the shops in the outer market close by the early afternoon). 
After navigating through the narrow alleyways of the "outer market," you can explore the "inner market." Known as jōnai-shijō, the inner area is the licensed wholesale market, where the auctions and most of the processing of the fish take place, and where licensed wholesale dealers known as oroshi gyōsha (approximately 900 of them) operate small stalls. The actual auction is restricted mainly to buyers, however small groups of tourists are accommodated on a limited basis. Those who wish to see the auction, have to apply at the Osakana Fukyu Center (Fish Information Center) at the Kachidoki Gate, starting from 5:00am on a first-come, first-serve basis (may start earlier on busy days). Here are my pictures from the "inner market."