We went on our final morning. Our goal was to find antiques/unique items, not merely peruse a swap meet scenario. There are both types in the market which is VAST. Addresses online vary (due to the large set of blocks it encompasses, so it took a while (asking folks) what region of the market had the antiques. Thankfully we did not give up! Antique vendors have a specific section (mixed in were some vintage clothing, jewelry, etc), vs. other sections of the market were basic "tianguis" goods i.e. new socks, underwear, belts, menswear, quinceanera dresses, hello kitty, used books, etc.
Definitely be sure to brush up on your Spanish (duh), be polite, be fair in your offers. We wished we had more time, but were able to buy a handful of things in the 60-80 minutes we had. Mementos, some necklace pendants, a vintage 50s jacket, etc.
There was delicious taco stand and a fresh coconut juice stand we enjoyed. Prices were very reasonable. Various websites listed the opening hours differently (1 hour interval/gap), so we arrived halfway between. Definitely glad we made it, since it is only on Sundays. This was the most traditional of the markets we went to.
Other markets we attended were the punk market El Chopo (which didn't have as much selection as we had hoped, a lot of repetition of Hot Topic type of items found in the US, Adios Closet Bazar which is a monthly vintage clothing market (good stuff), and a street "tiangius" in Condesa (near Lardo) that had a lot of fresh fruit and vegetables.