How did the Medici originally get into finance?

https://en.wikipedia.org/wiki/Medici_Bank#Founding

The Medicis are said to originate in Mugello, north of Florence, where they were modestly wealthy land holders. A Medici was a Signori of Florence in 1301, though not of the same branch. The origins of the Medici bank can be traced to Viero de Cambo, a distant cousin of Giovanni. He became a successful banker during the turmoil following the Black Death. It's not a stretch to connect their beginnings with this disaster. Giovanni and his cousin Fransesco were trained in the banking house of Viero de Cambo before becoming partners in the firm. Giovanni became general manager of the Roman branch in 1385, which was incorporated as a partnership. His bank was well funded by the Holy See. Viero di Cambo continued in banking, but Giovanni's bank emerged as the most successful enterprise (probably because of his patronage of the Vatican). In 1397 he moved the bank to Florence.

1378, while the oligarchy was strained by a war with the Pope, Giovanni's cousin Salvestro di Medici was a part of the Ciompi worker's revolt. It placed him and a group of non-nobles in charge of Florence for 4 years. This was not necessarily connected to Giovanni, but it's an early political attempt by a Medici. In 1400, Giovanni Medici himself was implicated in a plot to open the gates to the Visconti. In two years, the leader of the anti-Medici party died of the plague, and the Visconti captured Florence and Pisa. The Visconti domain collapsed, but altered the politics of Northern Italy. It was at this time that the Medicis branched out over Italy, first starting a bank in Venice in 1402, then Naples. Also the Medicis opened up two wool proccessing plants (Florence's key industry). In 1414, the Avignon Papacy moved back to Rome.

In 1298, the success of Florentine banking sent the Bonsignori family of Siena into bankruptcy. Florence surpassed Siena as the banking center of Italy. This shift was a factor in the later expansion of Medici banks throughout Italy.

The answer is not so much a specific list of steps (task-list) but more Cosimo's political maneuvering, with family and friends, that propelled him leadership in the Republic of Florence.

His political ability resulted in real political power, which propelled their name into history. What he actually did, in most observations, is not explicitly stated -- it was more how he thought (his approach) -- that made it work for the Medici family.

On political ability, p. 1262:

On the surface, it seems obvious that Cosimo de' Medici (1389-1464) did it all. Cosimo de' Medici was multiply embedded in complicated and sprawling Florentine marriage, economic, and patronage elite networks. And he was riding herd on vast macropolitical and macroeconomic forces far beyond his control. Yet he founded a dynasty that dominated Florence for three centuries. He consolidated a Europe-wide banking network that helped induce both international trade and state making elsewhere. And he oversaw and sponsored the Florentine intellectual and artistic efflorescence that we now call "the Renaissance".

On political power, p.1262:

Contemporaries deeply appreciated Cosimo's power. Foreign princes after 1434 flocked to Cosimo's private palazzo to work out international relations, much to the consternation of bypassed Florentine officials. Cosimo was legally enshrined on his death as the father of his country-no mean recognition from citizens as cynical and suspicious as the Florentines.

On thought process (approach), p. 1263:

We use the term "robust action" to refer to Cosimo's style of control. The key to understanding Cosimo's sphinxlike character, and the judge/ boss contradiction thereby, we argue, is multivocality-the fact that single actions can be interpreted coherently from multiple perspectives simultaneously, the fact that single actions can be moves in many games at once, and the fact that public and private motivations cannot be parsed ... Moreover, especially after 1434, all action by Cosimo (never explained or rationalized) appeared extraordinarily reactive in character. Everything was done in response to a flow of requests that, somehow or other, "just so happened" to serve Cosimo's extremely multiple interests.

On Cosimo's style, p. 1263, fn.8:

Contemporaneous reports of Cosimo's personal style are as fo!lows: "He acted privately with the greatest discretion in order to saieguard himself, and whenever he sought to attain an object he contrived to let it appear that the matter had been set in motion by someone other than himself. . He replies were brief and sometimes obscure, so that they might be made to bear a double sense" (Vespasiano [ca. 149S] 196.3, p. 223). "In 14.32, just before his exile and triumphant return, a political opponent, Francesco Filefo, described in a letter how Cosimo, in contrast to his 'open and lighthearted' brother, Lorenzo, 'is, I notice, despite appearing devoted to me, the kind of man who feigns and dissembles everything. He is so taciturn that he can scarcely be understood even by his intimates and servants in his family circle' " (Brown 1992, p. 106).

Source: Padgett, John F; Ansell, Christopher K, 'Robust action and the rise of the Medici, 1400-1434', The American Journal of Sociology; May 1993.

Cosimo di Medici inherited a thriving "banking" business from his father Giovanni, who was the "Fred Trump" of the family, with Cosimo being like the current President of the United States. Most people "get into" something by starting small; a smart or lucky few get "big" and become very successful.

Giovanni had inherited a small time moneylending business from his father, and "apprenticed" with bankers in Florence to learn the banking business. After that, Giovanni had the brilliant idea of what we would now call "branch banking," starting branches all over Europe including London, Bruges, Avignon, Venice, and especially Rome. In the latter place, the Medicis became the bankers, then the money managers, and finally commodities traders for the Vatican, which gave them a lot of cachet. Cosimo took his profits from Rome (which was more profitable than the rest of the network put together) and reinvested them in Florence real estate, making him the dominant figure/wealthholder in that city.

Cosimo had an undistiguished son, Pierre the Gouty, who, however, produced an outstanding grandson, Lorenzo the Magnificent, who turned the family's economic power into de jure (not just de facto) political power. Thus, the family maintained most of its power even after it lost some of its wealth through bad investments.