The farmers market
The Thai Agriculture Ministry's demonstration market is, both literally and figuratively, one of the most accessible fresh markets in Bangkok. Literally in that one exit from the Kampangphet subway station is right inside the market. Figuratively speaking, the market is a lot less dark and grotty than most fresh markets, especially since an extensive upgrade was completed in 2009. In addition, since the Aw Taw Gaw market is right across the street from the Chatuchak market, they're used to the occasional tourist wandering through, so you may see some signs in English as well as some stall owners that have rudimentary English skills.
The clean and well organized look of the market is down to the fact it's run by the Ministry of Agriculture as a sort of demonstration market. In other words, this is what fresh markets are supposed to look like. You can get a dose of reality at any other fresh market in Thailand. That said, this is not a "Disneyfied" market that's all show and no substance. This is definitely a real and functioning market, used by many Thais. In fact, the market has something of a reputation for having things, like yellow mangoes, when they're generally out of season and not carried in other markets. In addition, many of the stalls are adept at packing fruits and sweets for shipment, so if you're lucky enough to be from a country that still allows you to bring in fresh fruit, you can get it nicely packed and strapped into easy to carry boxes.
The market carries a wide variety of items, from fresh meats and seafood, to fruits, vegetables, dry goods like rice, and a large selection of sweets. There's also a small collection of food stalls, which makes the market one good option for eating if you're visiting Chatuchak and get hungry. Unlike Chatuchak, the Aw Taw Gaw market is open every day, from early morning until the evening.