Zielinski
ZIELINSKI is normally spelled with an accent over the N and pronounced roughly "zheh-LEEN-skee." It's one of many Polish names that are so common and so widespread that there is no one derivation. As of 1990 there were 85,988 Polish citizens named Zielinski, living in large numbers all over Poland. It is the 7th most popular Polish surname! There isn't one big Zielinski family that got the name one way, there are many families who all got the name independently in different ways. If you were in a big room full of Zielinskis, you would probably find this Zielinski family got their name one way, that one another, and that one yet another.
The most we can say is that the basic root of the name is ziel-, which means "green," as seen in words such as ziolo, "herb" (a "green"), zielen, "the color green," and so on. So ZIELINSKI may have started in some cases as referring to the kin of a fellow who raised or sold herbs, or a fellow who always wore green, or some other perceived association between a person or family and something green.
In most cases, however, it probably started as a reference to the name of a place the person or family came from. There are many towns, villages, estates, etc. with names like Zielen or Zielin or Zielina, all from the root meaning "green," and Zielinski could refer to any of them. It can just as easily mean "one from Zielen", "one from Zielin", "one from Zielina", etc.
So there's no way to learn from the name itself anything about a given Zielinski family. Only successful genealogical research may uncover facts about which particular place the name refers to, if it refers to a place, or what the family's connection to "green" originally was, if it doesn't.