A K-1 visa allows a U.S citizen to bring a fiancé (and the fiancé's children, if any) into the United States in order to get married. The K-1 visa lasts for 90 days and cannot be renewed. For some couples, that's a long enough stay in the United States, and they leave after the wedding.
More often, however, the immigrant fiancé wishes to apply for a green card after the marriage. This is possible using a process called Adjustment of Status.
Adjustment of Status or "AOS" refers to the process of applying for a U.S. green card (permanent residency) within the United States. It involves filing a bunch of forms and documents with U.S. Citizenship and Immigration Services (USCIS), having fingerprints (biometrics) taken, and attending an in-person interview (both spouses, together) at a USCIS office.
Because the K-1 fiancé visa is not renewable, the need to adjust one's status puts some time pressure on the couple. You'll need to not only get married before the 90 days is up, but make sure that you'll be able to receive an official certificate of your marriage from a local government office before submitting the adjustment application. (A church certificate or non-certified document won't be enough for USCIS.)
And of course, you'll need time to prepare the various immigration forms and documents, get English-language translations of certain documents, and possibly get an attorney to help.
The primary form that the immigrant spouse will need to submit is Form I-485, Application to Register Permanent Residence or Adjust Status.
Another important form that goes along with this is an I-864 Affidavit of Support, prepared by the U.S. citizen petitioner, with supporting documentation. The I-864 shows that the U.S. citizen spouse has the financial capability to make sure the immigrant won't need to receive government assistance, in other words become a "public charge." In fact, it's a contract with the U.S. government promising to support the immigrant for approximately ten years (regardless of divorce).
Be sure to also include a Form I-765 if the applicant would like to have a work permit (employment authorization document).
The immigrant must also submit a medical examination report on Form I-693 (if the one done for the consulate is over a year old by this time), a long-form birth certificate (translated into English, if need be), a copy of the immigrant's I-94 Arrival/Departure Record, a copy of the I-129F petition approval notice from USCIS, a copy of the marriage certificate, and two color photographs of the immigrant (passport style, meeting DOS requirements).
USCIS collects large fees to file these applications. You can either pay by credit card using Form G-1450, Authorization for Credit Card Transactions, or write a check or get a money order for the required filing fee.
Then prepare the packet for mailing. You can't submit the AOS application in person; it must be sent to a particular USCIS office.
After the I-485 packet has been submitted, you'll get a receipt notice from USCIS. Later, the immigrant will be called in for fingerprinting ("biometrics"). Many months after your initial filing, you'll be called in for the interview.
Assuming all goes well up through the USCIS interview, and the interviewer approves the immigrant's application, the immigrant will become a "conditional resident." That's almost like getting a regular green card (permanent resident), except that this status basically runs out after two years. The legal rationale is that, for such a recent marriage, the U.S. government wants a second chance at making sure it's bona fide, not just a fraud or sham to get someone a green card.
You'll see the expiration date on the immigrant's card.
So, the immigrant will need to keep track of the two-year anniversary date and, up to 90 days before those two years is up, file to convert from conditional status to permanent resident status. This is done using USCIS Form I-751.
Adjusting a spouse's legal status from fiancé to permanent United States resident can be tricky. Having an immigration lawyer provide experienced guidance on the process can avoid unnecessary delays and complications.