The K-1 fiance(e) visa allows a fiance(e) of a U.S. citizen to come to the U.S. and get married. Since the fiance(e) is not yet a spouse of the U.S. citizen at the time the visa is issued, the K-1 visa is technically a non-immigrant visa. But since the purpose of the visa is to allow marriage in the U.S., it is treated in many ways like an immigrant visa by many Embassies/Consulates.
Once the fiance(e) enters the U.S. with a K-1 visa, s/he must marry the petitioning U.S. citizen within 90 days. Otherwise, the fiance(e) will fall out of status and be required to leave the U.S. Once a K-1 fiance(e) loses his/her status, there is no way to "fix" the situation in the U.S.; even if the fiance(e) marries a different U.S. citizen, the fiance(e) cannot adjust status in the U.S., i.e., cannot apply for permanent residence in the U.S. If the fiance(e) married the petitioning U.S. citizen outside the 90-day time limit, the fiance(e) has to return to his/her home country and the U.S. citizen spouse must file a Form I-130, Petition for Alien Relative.
Another thing to keep in mind is that the fiance(e) can enter the U.S. only one time with a K-1 visa; if s/he leaves the U.S. before getting married and wants to come back to the U.S., s/he will have to apply for and obtain a new visa.
If the fiance(e) intends to live and work permanently in the U.S., s/he can apply to adjust status (to become a permanent resident) after the marriage. If the fiance(e) does not intend to become a permanent resident, s/he has to leave the U.S. within the original 90-day period.
Requirements
1. You (petitioning person) must be a U.S. citizen. There is no visa category for a permanent resident's fiance(e).
2. Both you and your fiance(e) must be free to marry. In other words, both of you must be unmarried; any previous marriages must have ended through divorce, annulment, or death; and there must be no other legal obstacle for marriage.
3. You must have met your fiance(e) in person within the past 2 years before filing your I-129F petition. This requirement can be waived, only if meeting your fiance(e) in person would violate long-established customs or meeting your fiance(e) would create extreme hardship to you.
How to apply
1. You (U.S. citizen petitioner) must file a Form I-129F, Petition for Alien Fiance(e), along with supporting documents, with USCIS.
2. Once USCIS approves your I-129F petition, the approval will be valid for 4 months only, during which time your fiance(e) must apply for and obtain a K-1 visa at a U.S. Embassy/Consulate. Your fiance(e)'s unmarried, under-21 children can apply for and obtain K-2 visas. The U.S. Embassy/Consulate may extend the 4-month period if processing of the visa application would require more time.
3. Once the U.S. Embassy/Consulate issues a K-1 visa, the visa will be valid for 4-6 months only, during which time your fiance(e) must arrive in the U.S.
4. Once your fiance(e) enters the U.S., you and your fiance(e) must marry within 90 days.
5. If your fiance(e) (now your spouse) and his/her children want to work and live in the U.S. each of them has to file a Form I-485, Application to Adjust Status, with USCIS (one I-485 per person). K-2 children must apply for and obtain their green cards before they turn 21.