1. Marry in the U.S. and change the status in the U.S.
If you are married to a U.S. citizen or Legal Permanent Resident ("LPR": Green card holder) in the United States, you can apply for LPR based on the marriage. The most common question in this case would be if the foreign spouse can apply for LPR process after entering the U.S. with ESTA ("Electronic System for Travel Authorization") which is valid only 90 days. Since ESTA is digital travel authorization to travel to the U.S. without a visa, it is not any immigration status for applying the green card process. However, there is an exception: IR (Immediate Relatives: spouse, parents, and minor children) of U.S. citizen can apply for the LPR process from ESTA. Accordingly, entering to the U.S. with ESTA and marriage & file the I-485 application within or after the 90 days would be a valid option for a spouse of U.S. citizen. You can change your status as a LPR in the U.S. even if you have a record of illegal stay or illegal employment. Please note, however, that this benefit does not apply to spouses of LPR.
The LPR status acquired by the marriage is a conditional status which is only valid for two years, therefore you must take a step with your spouse for removing the condition by filing the petition (USCIS form I-751) together 90 days before the two-year anniversary.
2. Marriage After Entry into the U.S. through a Fiancé’s Nonimmigrant Visa (K-1)
The K-1 fiancé visa issued to the fiancés of U.S. citizens (not LPR) who are living outside of the United States. The K-1 visa is for the foreign fiancés to get married within 90 days of arriving in the United States.
The most critical requirement for K-visa is that a petitioner (a U.S. citizen) should prove that they have met at least once during last two years. If the U.S. citizen can prove this condition, he/she will submit an I-129F petition to the USCIS in the U.S. Upon the approval from the USCIS, the U.S. Embassy in the fiancé’s home country receives the approval document through the NVC (National Visa Center), it notifies the fiancé lives in the foreign country and sends the interview date. At the interview for K-1 visa, the most important questions are when, how and where the two people came to know each other. If there some pictures taken at the time of the engagement ceremony/ travels/ family events or e-mails, texts, or other letters exchanged with each other, it is recommended to bring them to the interview examiner. If the fiancé has children under the age of 21, the children may enter the United States on a K-2 visa.
The K-1 visa holder who enters the United States as a fiancé must marry the U. S. citizen (petitioner) within 90 days of the entry. If the K-1 visa holder does not get married within 90 days, or if marry someone other than the U.S. citizen who invited you, the K-1 visa holder should leave the U.S. right away. Otherwise, the K-1 visa holder will be given a deportation order. If married within 90 days, the K-1 visa holder will be eligible to become a permanent resident so that the foreign spouse can file an I-485 application with a valid marriage certificate to change status from K-1 to LPR.
3. Enter the U.S. with a conditional green card (i.e., CR1) after Marriage
If a K1 visa is a U.S. citizen's fiancé who will be married to a US citizen before marriage is filed, the CR1 visa is a "spouse" visa that can be applied as a spouse of a US citizen in their home country when the foreign spouse cannot stay in the U.S. For instance, if the foreign spouse has a job and cannot quit the job right away, the U.S. citizen or LPR living in the U.S. files petition to invite the spouse. To apply for CR-1 visa with the invitation of a spouse of a US citizen, you must proceed with marriage registration first either in the U.S. or in the spouse's home country. Once the petition filed by the U.S. citizen/ LPR spouse, the U.S. Embassy in the fiancé’s home country receives the approval document through the NVC (National Visa Center), just like K-1 visa process above. After an interview at the U.S. Embassy, the foreign spouse will be able to enter the U.S. with the CR-1 visa as a conditional permanent resident. The CR-1 visa itself is valid for 12 months until the green card is issued and received. In some weeks from the arrival, the foreign spouse receives a green card that is valid for two years to the mailing address in the U.S.