The most obvious difference between the Black Market and a normal shop is that you will be vastly overcharged for items. The prices for almost all items including all magical items are 50 times normal, and the prices for other items are 25 times normal. You can sell items at the usual selling price, and the shopkeeper has more money than other shopkeepers, but by the time you reach the Black Market, you probably no longer need gold.
The shopkeeper, One-Eyed Sam, is much tougher and better armoured than other shopkeepers. He is equipped with a long sword named Thiefbane, gray dragon scale mail, a shield of reflection, speed boots, and an amulet of life saving, and his weapon and armour tend to be highly enchanted. He is also stoning resistant. Thiefbane has a 10% chance per hit of beheading you and a 15% chance of cancelling you, as well as the ability to drain levels.
You are not permitted to enter the Black Market while polymorphed, although there are no longer any other restrictions on the use of polymorph on that level (so you can enter and then immediately polymorph). The Black Market is also a no-teleport level.
Since the prices in the Black Market are so high, it is not practical to buy the items you need. I have come across four workable strategies for stealing from One-Eyed Sam: in order of increasing risk, they are to shoplift the Black Market with the aid of a pet or to acquire large amounts of credit (thanks to David Throop for this strategy), to grab the stuff you need and run, and to kill him.
To shoplift the Black Market, first go through everything in the shop sorting it into things you want and things you don't. Pile the things you don't want in a corner, and arrange the things you want around the door, along with One-Eyed Sam's tripe rations. Then have your pet steal everything in the normal way.
This is a low-risk strategy, but it is rather slow, and there are three points to watch when using it which don't cause problems if you're robbing Sam or killing him.
If you get your first chunk of credit before doing anything else in the Black Market, you'll be able to consume some of Sam's property while sorting through it, which is an advantage over the shoplifting strategy. Waiting for the right type of hostile monsters sounds rather slow, though. You could also steal credit with the aid of a reasonably strong pet - put all your gold in a spare bag and have your pet repeatedly steal the bag.
Here's a step-by-step guide to this strategy.
Jackson Simth has suggested a refinement to this strategy. If you can cast the spell of passwall, or have some means of controlled polymorph, then after grabbing everything you want, you can walk out through the wall and straight into the portal. The hordes of soldiers will still be summoned, but won't have a chance to go through the portal.
Matt Roe points out another refinement: ``the Eye of the Aethiopica will not work inside the market but it will work one step outside the door'' so after teleporting Sam and running out of the door, you can invoke the Eye and get well away from the hordes.
Taking Sam on in melee combat is extremely dangerous, especially if you lack level-drain resistance. Kristopher J Preacher has suggested a safer way to kill him. First use conflict to make the assistants kill each other, then read a few scrolls of earth and surround Sam with boulders. You can now safely kill him from afar, and he won't be able to touch you. He does not resist poison, so one way to kill him from afar is with poison darts (thanks to Alan Beck for this suggestion).
If you have to melee Sam, disarm him as soon as possible, either with the disarm technique or with a bullwhip. It also helps to attack him from outside his shop so that you can retreat at will. It appears that if you are invisible, then once Sam is hostile he will never move from his spot in front of the doorway. This helps you because when you retreat from the doorway, Sam still stands there, blocking his assistants from chasing after you. They can still use their ranged attacks, but you can prevent this by closing the door. No-one will open it, so you'll have all the time you need to heal. If you are not invisible, Sam can follow you out of his shop. He doesn't open doors himself but his assistants do.