The biggest market is on the north side of the Rialto bridge. There is an outdoor vegetable & fruit market with the most wonderful produce you can find. It is open Monday through Saturday from 8:00am to 1:00pm. The fish market (Pescheria) is indoor and offered a wide selection of fish, calamari, shrimp, shellfish, etc., some of them still alive, at price lower than the US. The fish market closes on Sunday and Monday. Meat is to be bought from nearby butchers w/ price higher than the US. Try to learn a few italian words such as numbers if you plan to be shopping at the market. Tip: "etto" = 100gr.
Scattered small markets or vegetable stands can be found on Stranda Nova (in Cannaregio), Campo Santa Marguerita (San Polo), Piazza Santa Maria Formosa (Castello), etc.. There is a floating vegetable & fruit market on Campo San Barnaba (Dorsoduro), not far from Accademia and Campo Santa Marguerita. Take Vaporetto #1 to the Ca' Rezzonico stop and Campo San Barnaba is at the end of the short alley.
There are also several "American-styled" supermarkets but they are much smaller than the ones you find in the States. The supermarkets have much longer hours than the outdoor markets. The most central one is SuVe (Supermarket of Venezia) on Salizzada San Lio in between San Marco and Rialto, and a few doors from the famous Boutique de Gelato. The Standa department store in Cannaregio also has a supermarket in the back of the store. For meat however, you still have to visit one of the butchers. There are 2 near SuVe. Shopping at the supermarkets is less fun but more stress-free if you do not speak italian since they are predominantly self-serve. The way to buy fruit and vegetable is to note the number designating the produce from the sign, put the goods on the scale, punch in the number and a sticker with the total price will be come out.