A lot of people who enter the United States in order to work wind up getting a non-immigrant visa, but if they receive a job offer while in the country they can put in an application for permanent residency, or in other words apply for a green card.
There are a number of different paths that can be taken to get a green card, and which is the right one for the individual concerned very much depends on what their personal circumstances are. If they have been offered permanent employment in the United States by an American business, for instance, they may be able to put in an application for permanent residency, in which case the employer needs to have labor certification obtained from the US Department of Labor, which enables them to permanently hire foreign workers. Providing they have this, the employer can file an Immigration Petition for Alien Worker, Form I-140, on their behalf.
Entrepreneurs and investors who want to be able to develop an enterprise within the United States that is likely to result in the creation of more jobs can also put in an application for a green card.
If someone does not have an employer that can file the petition for them, they can do it themselves providing that they have been given a National Interest Waiver, which means that they have extraordinary skills that would be of benefit to the United States, or the O-1 visa that is given to Individuals with Extraordinary Ability or Achievement.