Good morning. The fiance visa (K-1) is issued to the fiancé of a U.S. citizen, your boyfriend, allowing that person to enter the United States. Once the foreign fiancé enters the United States, he or she can marry the U.S. citizen and then, if desired, apply for a green card under the immediate relative category. The technical name for the process of applying for the green card within the U.S. is Adjustment of Status.
But applying for a green card isn't required. Some fiancee's use this visa simply to enter the U.S. and get married, after which the couple lives in the non-U.S. citizen's home country, or somewhere else. As the spouse of a U.S. citizen, of course, the former fiance can always apply for a U.S. green card.
You must start off the process by filing United States Citizenship and Immigration Services (USCIS) Form I-129F, Petition for Alien Fiancé. The forms are available from the USCIS website.
In addition to Form I-129F, you will need to fill out and submit Form G-325A Biographic Information, and provide proof of U.S. citizenship and evidence of your courtship and meeting within the last two years. You will also need to pay the visa petition fee.
Once the petition is submitted, USCIS will review it for completeness, and within a few weeks, receive a Form I-797 Notice of Action acknowledging receipt of the petition. After that, USCIS will do a full review, and hopefully approve the petition and send you an approval notice.
USCIS then forwards the petition to the National Visa Center for conducting background checks and sending the fiance some visa application forms to be filled out. Once the background checks are completed and he has filled out and returned these forms, the file is transferred to the U.S. embassy or consulate having jurisdiction over the fiancé’s place of residence. Next, the embassy will then send him instructions for gathering additional documents, getting photographs made, having a medical exam done, etc.
The last step in the process is for the fiance to attend an interview at the U.S. consulate. This doesn't happen on a walk-in basis -- the consulate will send an appointment notice. At the interview, the fiance visa may be approved -- though it's likely that the actual visa issuance will be delayed a few days after the interview, pending final security checks. Once he receives the visa he can then travel and marry you.
I hope this helps.