Here is a brief summary of the different options:
Nonimmigrant Fiancée (K-1)
This is for you if: you are not currently married; and you intend to get married in the United States.
Here is the process:
1. You file a Visa Petition with the USCIS (I-129),
2. Your foreign fiancee has an interview at US Consulate abroad,
3. After you marry within 90 days of your fiancee entering the U.S., your fiancee files for adjustment of status to become a conditional permanent resident.
4. Within two years, your spouse files to remove the conditions, and he/she becomes a permanent resident.
Requirements include: You must have physically met one another in person at least once in the past 2 years. Also, travel to the US is likely limited – applicant may be required to remain outside of the U.S. until a visa is issued. Process for entering the US is about 3-8 months.
Nonimmigrant Spouse (K-3)
This is for you if: You are already married, and want to be together in the United States as soon as possible. After your spouse enters the United States, then you will seek to adjust his/her status to permanent resident.
In this process, you must first file a visa petition with the USCIS; and then your spouse must attend a visa interview at a U.S. Consulate. After he/she is admitted to the United States, you file for an adjustment of status so that your spouse becomes a permanent resident.
It is also possible to apply for permanent residency at the same time as a receiving a visa (which would be an immigrant visa).
Here is the biggest mistake: Don't have your fiancee or spouse enter on a tourist visa, and then try to convert to permanent residency. That involves misrepresenting your intent in entering the country.