First time I attempt to answer, please be gentle if I broke any rules mods. I probably did:

Until about 1931 with the end of the so-called Castellamarese War it was very hard for a non-Sicilian to become a made member of the mafia. The mafia as we know it essentially grew out of that war, before prohibition Italian-American crime groups were little more than street gangs. The Castellamarese War was an underworld conflict between two opposing groups, one led by Giuseppe "Joe the Boss" Masseria and one by Salvatore Maranzano.

Joe Masseria was the head of the largest Italian gang in New York in the mid 1920s, based in East-Harlem. Future underworld luminary Lucky Luciano worked for him, which is important for later.

Maranzano arrived in New York from Sicily during prohibition. He was a made member of the Sicilian mafia and hailed from the Castellemare del Golfo region, as did his inner circle. One name you might recognize who worked for Maranzano (and was also from Castellemare del Golfo) is Joe Bonanno, namesake of the Bonanno family in New York.

In 1930 Joe Masseria, as the premier Italian gang leader, started demanding tribute from independent Italian gangs(ters). The Castellemare faction looked to Maranzano for guidance and he refused to submit to Masseria's demands, which sparked the Castellemarese War.

The aforementioned Lucky Luciano (real name Salvatore Luciana) worked for Masseria but worried that the bloodshed would impede their ability to make money. He also resented Masseria for dismissing the business ventures he proposed, like coöperating with non-Sicilian (and even Jewish and Irish) criminals. After eighteen months of fighting Luciano approached Maranzano about switching sides. During a dinner at a Coney Island restaurant Masseria was gunned down. Luciano was also present, but he conveniently went to the bathroom just before it happened.

Maranzano seemingly emerged victorious. But he wanted to crown himself boss of all bosses, first among equals in the underworld, and Luciano wouldn't stand for that either. Several months later Maranzano too was killed by a group of hitmen who posed as IRS agents to gain access to his office. After Maranzano died, Luciano set up a Commission composed of the heads of the five largest Italian crime groups (three of which fell under the banner of either Masseria or Maranzano during the war). The Commission was set up in order to settle disputes between groups and prevent gang warfare. Any problems between members of different groups were to be brought to their immediate superior.who brought it to his superior until.it reached the commission, where a decision would be made. Luciano also made it possible for non-Sicilians to become full members of these groups, which earlier more traditional bossed had not allowed. The mafia as it existed in Sicily was much more clannish, some mafiosi even refused to closely associate with Sicilians who were from a different region (as was the case with the Castellemarese faction). So even the term mafia is tricky because the mafia as we know it didn't exist until the structure changed from loosely associated street gangs to the more corporate form that still exists today.

I will continue this later today if there's any interest because the question is so expansive, I haven't even answered it yet. Typing on phone is hard.

Source: Selwyn Raab - Five Families: the Rise, Decline, and Resurgence of America's Most Powerful Mafia Empires

This is based on personal knowledge and by reading some antimafia reports but I'm from South Italy and as far as I know the original American Cosa nostra worked the same way as the Sicilian one being created by immigrants born in Italy.

To cite Buscetta "You don't join the mafia, you get invited to it."

I don't know if this is still true, but anyway, to join from the outside you have to start your way in by being an "avvicinato", that can be roughly translated to "Someone who has been contacted" (not a literal translation).

Most of the people we think as "mafiosi" are just associates and joining the family it's not so easy.

An "avvicinato" is someone who has been contacted by a "Man of honor" (Someone who is inside the family) and, as far as I know, only southern Italian descendents could get into the family while other nationalities usually stay as associates forever.

Usually the man of honor has to know the avvicinato for many years, even 10/15 before his name can be considered and he is also going to be responsible for him.

So an associate start doing works like rackets, homicides, thefts etc for the family while not being in it and he gets studied for some time, a couple of years, when he is trusted enough he gets invited in it.

When he does these jobs, he knows basically nothing about the family.

In the initiation ritual (these can be differents) the associate gets taken somewhere with the heads of the local family and they decide if he gets in.

If he is "worthy", his trigger finger gets poked and his blood spilled on a small sacred image, like a Saint , after that this image gets burned in his hands while he recite a promise of loyalty to Cosa nostra and that "his flash may burn like the image if he ever betrays it".

When this is done he becomes a "Man of honor".

There isn't a recruitment center, you have to know people inside the family and be trusted by them or you will stay as an associate forever.

Sorry if this isn't a complete answer, but if you have any other questions I may be able to answer feel free to ask.

EDIT: If you are looking for typical early mafia crimes, check the "Black hand", the early Cosa nostra operated in the Italian communities especially with extorsions and thefts, after that they grew during the prohibition.

Small family anecdote, my father's grandfather, like many Italians, moved to the states at the start of the XX century but he came back as soon as he could.

His explanation was that the place where he lived was controlled by the mafia and his options were to pay them up or work with them, he didn't want to and came back to South Italy where, apparently, it was a lot easier to live without the mafia being around so much.

Sorry for my English and for various mistakes, I'm using my phone and I have a 3 languages on the keyboard that sometimes get mixed.

As source, most it is based on personal knowledge, we could say "cultural" unfortunately.

A good read about Cosa nostra structure is this one but unfortunately is in Italian.