There are a number of provisions which may make you eligible for a US green card. For example, your family, employment, job offer, investments in the US, refugee and asylum status, as well as many other things, may qualify you for a green card. Generally, to be eligible for a US green card, you must meet four requirements:
1) You must be eligible for a green card under one of the immigrant categories under the Immigration and Nationality Act (INA). There are several immigrant categories that may allow you to be eligible for a green card. For example, if you are the relative or immediate family member of a US green card holder or US citizen, that person can usually sponsor you for a green card.
2) You must have a petition filed for you and approved. Your family or prospective employer must generally submit a petition on your behalf, indicating that he or she is willing to sponsor you. Common petitions filed on behalf of applicants include Form I-140 (Immigrant Petition for Alien Worker), Form I-130 (Petition for Alien Relative), Form I-360 (Petition for Amerasian, Widow(er), or Special Immigrant), and others. In some cases, there are special categories which allow green card holders to apply for a green card themselves, without sponsorship. You can learn more about these categories on the USCIS website.
3) There must be an immigrant visa available for you. Each year, Congress sets up a specific number of eligible visas for every immigrant category. For example, non-immediate relatives of US citizens are granted so many visas. In cases like these, you may be given a priority number and you will be contacted when a green card is available for you. This process can take months or years. In some immigration categories (for example, immediate relatives of US citizens) there is no limit on US visas and there are generally visas available at once.
4) You must be admissible into the US. Applicants for green cards must be able to prove to consular or immigration authorities that they are eligible to be admitted to the United States. Some security-related, health-related, and criminal issues may make applicants not admissible into the United States. If you are found not admissible into the United States, you may be able to file Form I-601 (Application for Waiver of Ground of Inadmissibility) or Form I-602 (Application By Refugee For Waiver of Grounds of Excludability) to waive admissibility requirements. If your waiver is denied and you are found inadmissible to the US, your request for a green card will be denied and you will not be allowed to enter the United States. Consulting with a qualified immigration attorney may be the best course of action if this happens.