In order to become a permanent resident of the US, you must apply through the UCSIS, which includes the following: (1) File Form 1485 Application to Register Permanent Residence or Adjust Status; (2) Pay applicable fees set forth in Supplement A of Form 1485; (3) File Form G325A Biographic Data Sheet (between the ages 14 and 79); (4) File Form I693 Medical Examination Sheet (not required if applying based on continuous residence since before 1972, or if you have had a medical exam based on a fiance visa; (5) Provide two color photos taken within 30 days (Form I485 has instructions); (6) File Form I864 Affidavit of Support (completed by sponsor); (7) File Form I765 Authorization for Employment (if seeking employment while the case is processed); and (8) Provide evidence of inspection, admission or parole into the US (Form I94, Arrival Departure Record).
There may be additional forms and other materials to submit if you were initially admitted as the fiance of a US citizen, if you are a Cuban citizen, if you have been a continuous resident of the US for a certain number of years, or other special circumstances.