As a general proposition, there are two (2) manners in which foreign nationals come to the United States; either temporarily or permanently. If a foreign national is coming to the United States temporarily, he will apply for a nonimmigrant (i.e., temporary) visa (unless he is visa exempt) in a nonimmigrant visa category that coincides with the purpose of his temporary stay in the United States (e.g., tourism, work, student, etc.).
A foreign national may wish to come to the United States permanently. If that is the case, then there are, again very generally, two (2) primary ways to do so: either by showing a qualifying relationship to a U.S. citizen or lawful permanent resident (i.e., a “Green Card” holder) or by having an employer sponsor the foreign national for an employment-based Green Card. With respect to the latter, there are also ways in which a foreign national can “self-petition” for himself. Those situations are beyond the scope of this chapter beyond briefly mentioning them.
The Green Card is an expression that refers to the document carried by a lawful permanent resident, which provides proof of his or her status. There is actually no such thing as a “Green Card”.