I can’t answer this question for Europe, which is I suspect what you are interested in, but I can give some information about China from James Cahill.

First, in the Late Imperial period (Cahill’s data is mostly from Ming and Qing) the common myth was that great painters were literati amateurs. They were uninterested in the affairs of the world in general, and certainly not painting for money or painting to order. If I can risk a short quote. The master immerses himself in old books, not caring whether it is cold or hot, living tranquilly, uttering few words, magnanimous in disposition, his mind fixed on distant goals [that is, unconcerned with day-to-day affairs]. Pg.4

Note that this is quite different from the tradition in the West (which I mostly know from Cahill’s comparisons). There were court painters in China, but they were not regarded as artistically important. There were people who sold paintings in the marketplace, but they were hacks. My understanding is that in the West the myth of the autonomous artist who created for their own reasons, and who might sell paintings, but was not producing for a market, only came much later. Cahill calls Ni Zan the paradigm of the cultivated amateur in Chinese painting, and he died in 1375. Cahill points out that this myth has had a tremendous hold on the study of Chinese art both in China and outside, but it is a myth, and artists did make a living in a number of ways.

They might trade paintings for cash or other considerations (medicine, a place to live, political favors). This was often done in writing or through some sort of go-between, and the less famous the artist was the more likely it was the artist would have to put up with the buyer telling them what to paint and setting an exact date for it to be done by. We have a number of letters between artists and buyers complaining about late payment, late delivery, or that the painting was not what was ordered. Wealthy people needed a lot of paintings, to decorate their homes (often in rotation, so you needed a lot of them), as gifts or commemorations of a marriage or retirement, illustrations of a favorite poem, portraits, religious paintings, pornography, there was demand for all of these. Selling paintings in the street was considered crass, so only the desperate would do it. Painting to order was also considered low. Still, some artists posted price lists (by sizes) and there seem to be a lot of paintings that were quickly dashed off by major artists to sell or use to pay off social debts or with the idea they would eventually be sold. At least some artists suggested that opening selling paintings gave them more autonomy than living with a patron.

Payment might be in cash (this seems to have become more common over time), but gifts (moistening the brush) were more appropriate. Paper and silk to paint on, inksticks, wine (artists were supposed to be big drinkers) food, valuable antiques, courtesans, there are stories about all of these being exchanged for paintings. A painter could also become an artist-in-residence. This might be presented as an amateur artist staying with an admirer for a few days and gifting him a few paintings or some calligraphy. Or it could be a more long-term relationship where the artist was expected to produce on demand for an extended period. Ren Xiong lived for a while with a patron who had him paint playing cards for a party he was hosting. This may seem rather low for a great artist, but the guests were so impressed with his work that he got some commissions out of it, so all’s well that ends well.

Of course if you commissioned or bought a painting it may have been done in part or in whole by an apprentice or other person working in the artist’s studio. There were also ghost painters (not people who painted ghosts, more like ghost writers). They might be people who produced painting for others to claim as their own. All members of the elite were expected to be able to paint and a painting (or calligraphy) from the brush of a powerful figure was an important sign of political favor. If he could not produce all the paintings he needed…maybe hire someone. Well known artists also sold work done by others under their own name.

So while the ideal was that a Chinese artist was independently wealthy (or poor and did not care) and painted only what moved or amused him, in practice they produced for a market, although they tried to preserve an appearance of autonomy.

Sources Cahill, James. The Painter's Practice : How Artists Lived and Worked in Traditional China. Bampton Lectures in America. New York: Columbia University Press, 1994.