Once your fiancé has entered the United States on a K-1 visa, you must get married within 90 days of your fiancé's arrival in the United States. Once the marriage takes place, your spouse must file Form I-485 (Adjustment of Status) with the USCIS.
The petitioning spouse, either an American citizen or a lawful permanent resident (Family Second Preference category), is referred to as the Petitioner; the immigrant spouse is referred to as the Beneficiary when filling out the forms.
The Petitioner must file an Affidavit of Support with the Beneficiary's Form I-485 application for the Beneficiary to become a lawful permanent resident. Upon approval of the I-485, the Beneficiary will be granted a Conditional Status Green Card, valid for two years.