It depends on what you want or need from them.

You may need help getting capital for your business, and you may be too risky/have too little collateral for a mainstream lender. In that case, you would need to connect to a loanshark, likely through an acquaintance of an acquaintance. I’m not sure how the initial contact would go, but essentially, you would ask to borrow money at an exorbitant rate. If you don’t pay back on time and in the promise amount, the mob-backed loanshark would likely turn to threats and then actual violence.

In 1970, former US Attorney General Ramsey Clark believed that loansharking was the #2 mob business in most cities (after gambling and before narcotics).

Even if you don’t need money, you may be the target of extortion. In this case, you would not approach the mob—they would approach you. The most basic instance of this is the “protection racket,” in which the mob associate says words to the effect of, “lovely dry cleaners you have here. It would be a shame if anything happened to it.” The crudest protection racket is threatening immediate vandalism or fire, but there were more subtle versions as well: the mob boss could make problems with the city liquor board go away, ensure that produce is delivered on time, and guarantee that the business got garbage hauled away.

If you have a restaurant, you may want jukeboxes. You will probably deal with a mob associate for that. Want to buy fish? You may be dealing with the mob. And it’s not just seafood—in the 1920s and 1930s, one Mafioso, Ciro Terranova, did such a good job of cornering New York’s artichoke market that he became known as the “Artichoke King.” Cigarette vending machines? Also the mob. In general, many of your vendors might be organized crime operations or themselves paying protection money to the mob.

If your business requires union labor, you may have to contract with a mob-affiliated union, or pay a mob-linked “labor consultant” to make your union problems go away.

Now, if your business is successful, you may discover that you have a new business partner. According to veteran crime investigator Virgil Peterson (1983), “ofttimes underworld characters have merely walked into an establishment and declared themselves ‘in’ for a certain percentage of the business” (435). One of the biggest concerns at the time was organized crime’s “infiltration” into legitimate business. This had been a known issue since the Kefauver Committee’s investigations (1950-1). A 1969 IRS study reported that 98 out of 113 mob leaders had known interests in legitimate businesses, including casinos and nightclubs (32), real estate (17), hotels (11), vending machines (10), restaurants (8), trucking (8), wholesale food (7), sports and entertainment (7), and banks (6) [source: Peterson, 434-5].

As to how to stay on their good side, the answer is simple, no matter how you engage with the mob: money. Goodfellas (1990), based on the real-life story of Henry Hill, provides a NSFW window into what your friendly neighborhood mobster wanted from you: https://youtu.be/3XGAmPRxV48

How much money are we talking about? In 1967, the President’s Organized Crime Commission estimated organized crime’s annual net income (not gross) at $6-7 billion—in an era when GM boasted net income of $1.6 billion a year. Others estimated the mob’s annual take as high as $26 billion (Clark, 73).