The two most significant examples of a black-market in operation during WW2 occured in the UK and Germany (immediately post-war).
In the UK, the black market arose through shortages due to rationing. In post-war Germany, especially in Berlin, the black-market arose from the same crippling shortages, but the black marketeers were, in the main, members of the victorious/occupying forces. E.g a soldier could buy a carton of cigarettes at the PX for 50 cents and sell them on for, perhaps, $100. Russian troops would pay well over the odds for a good wristwatch etc.
Essentially, the black market was a criminal enterprise. As such, secrecy was all important. The required secrecy was made easier by the fact that the purchasers of black-market goods were, in effect, breaking the law just as much as their suppliers. In addition, the arrest and removal of a black marketeer meant that his/her customers were deprived of the goods they needed/wanted.
The black-market was supported by theft, or fraud. That is to say, the goods were either stolen directly, or "diverted" from their designated destination. One is black, the other is the opposite of white.
The theft of goods occured, mainly, at places where a great deal of materiel was to be found - e.g. docks, rail-yards. Because of the fact that there were usually guards at such places, the theft usually involed small quantities. Greater quantities of goods were made available to the black-market through corrupt "officials" - those with access to the goods and the ability to cover-up their loss (through falsified paperwork etc). These could be civilian administrators with responsibility for the distribution of goods to the local populace, or serving members of the forces involved in the supply-chain to troops.
Bribery was an important tool in the black marketeers armory, especially since, once an official had accepted a bribe to "turn a blind eye" to the removal/sale of goods, he/she was complicit in the crime and at risk of arrest and prosecution.
The thing to remember about the black-market is that a great many people used it - people of all ranks and from all walks of life.
The "supply-chain" was, usually, fairly straightforward: the supplier obtained the goods and either sold them direct to the customers, or sold them on to others who would then sell them to the customers.
A word of caution. Poland was an occupied country. Therefore, black-marketeers put themselves at great risk. In the UK, a black-market "spiv", if caught, would be fined, or sentenced to a few weeks in prison. In occupied countries, convicted black marketeers could expect to be sent to a concentration camp, or even to face a firing squad. As in all enterprises, the gain had to outweigh the risk. It was one thing to sell a few cigarettes in a London pub and quite another to do so in an occupied country where the black marketeers had to contend not only with local law enforcement, but also with the German Feldgendarmerie (military police). Of course, if members of the occupying forces were complicit in the black-market, the marketeers could hope for some form of protection, but, as always "sauve qui peut" was the overriding maxim. In Poland they also ran the risk of being betrayed by people wishing to curry favour with the occupying forces, or who held Nazi sympathies. There were a great many people of German descent in Poland.
Tocotin is correct in saying that the chief black-market goods in occupied Poland were the basics of human existence - food, clothes etc. Any traffic in "luxury goods" was usually restricted to within the occupying forces themselves, or their trusted sympathisers. Be that as it may, it wasn't all that uncommon for German soldiers to sell food, alcohol, or tobacco to the local people - often at exorbitant prices, or in return for sexual favours.