People can become legal permanent residents (green card holders) through certain family members. In order to start the process, the US Citizen or green card holder must file a petition for the person seeking to become a legal permanent resident. Even when the petition is approved, the person seeking the green card will likely have to wait for a green card (visa) to become available.
The United States Citizenship and Immigration Services (USCIS, formally known as INS) allows for so many visas per year. Five countries (China, India, Mexico, Dominican Republic and the Philippines) are oversubscribed which means that at some point people from that country received more green cards (Visas) than they were supposed to and so people from those countries have additional wait times depending on their relationship to the family member that is petitioning for them.
If you are petitioned by what is referred to as an “immediate relative”, there is no wait time except the time that it takes USCIS to process the visa application. “Immediate relatives” are spouses of US Citizens, parents of US Citizens that are at least 21 years old or children under 21 years old of US Citizens.
If the person seeking their green card has spent any time in the United States illegally or entered the United States illegally, they may have other issues and should contact an immigration attorney to learn about their eligibility.