First, ensure that you are eligible to apply for a green card. Eligibility can be based on family, employment, refugee status, special immigrant status, being the victim of crime or abuse, through registry, and other special circumstances. If you believe this applies to you, refer to a more detailed list here. 

After determining eligibility, you must submit a green card application (form I-485) along with an immigrant petition, which is typically filed by someone else. There are various types of petitions that can be completed, depending on your situation. If you are eligible for a green card, you must determine if you need to apply through adjustment of status (if currently in the U.S.) or consular processing (if residing outside of the U.S.). Apply with the U.S. Citizen and Immigration Service (USCIS) for an adjustment of status, if you have an approved immigrant petition and a visa available, file Form I-485. If not, check if you qualify for concurrent filing (submitting the petition and Form I-485 together) with the U.S. Department of State. Once approved, you go to a biometrics appointment to provide fingerprints, photos, and a signature; and finally provide an interview. For a more in-depth explanation, instructions for specific situations, and the files you must submit, reference this page by the USCIS.