-Latex gloves. Thankfully, hubs likes "borrowing" items from the hospital, so we have a box under our kitchen sink for any particularly gnarly cleanups, but rubber kitchen gloves would do just fine. You're going to be sticking your hand into bins where you cannot see the bottom, so these come in handy. To be honest, I wasn't as grossed out by the bins as I thought I'd be after reading Cheap Jap's description. They're only about 10 inches deep, as opposed to the feet I was envisioning, but the gloves made the trip feel sanitary.
-Tissues (or a surgical mask.) Are you allergic to dust like me? Then realize (as I did not) that sorting through bins of musty clothing will stir up a dust storm like the Sahara has never seen. Wearing a surgical mask would have prevented my major sneeze attacks, but if you don't want to look like you've got SARS, popping a Claritin beforehand and bringing plenty of tissues is a good bet.
-Pull out interesting colors and textures. I wouldn't say this is the best place to find basics-- a J. Crew black tee looks just like that ripped XXL Mossimo shirt right next to it when they're all jumbled together. But a deep plummy wool pencil skirt just pops against the cheap synthetics. Same goes for a beautifully beaded Moth cardigan from Anthropologie. Let your eyes guide you (remember, you're wearing gloves. Check the fabric content later.)
-Let the ridiculously cheap prices allow you to experiment. While I wouldn't spend $15 + shipping on a plaid '80s power-shoulder dress on ebay, knowing it cost less than the subway ride over makes items that are total gambles less intimidating. Try a silhouette you'd be scared of in full-price, knowing that your find is infinitely better made than Forever 21, and about 1/5th the price.
-Know your measurements. This is the number one rule of thrift shopping, but since you are definitely not trying anything here on without a full-body Hazmat suit, write down your measurements on a slip of paper and keep it handy. Bring a cloth measuring tape to quickly check an item's size. Remember, fit varies, especially when you're looking at vintage items, so never rely on a size label.
-Bring your ipod. Seriously. Without music, I might have noticed my surroundings more and felt slightly self-conscious at the reckless abandon with which I was throwing clothing around in search of the perfect vintage dress (not that I overlooked the Hasidic shopper next to me, or the family of 6 eating lunch with latex gloves on.) Listening to my tunes, I got into a complete groove and was able to pretty decently cover the 20 or so bins.
-Remember the weight factor. Not for the prices-- because seriously, where else will you even find a heavy leather jacket for $3.00?-- but because you will be schlepping this stuff home. And you will take a lot because it is so cheap. Now that I think about it, bringing my own large cloth bag would have come in pretty handy, as all they give you is a flimsy plastic.
Hope these tips were helpful... now start digging!