The options vary depending upon whether the intend to marry before or after she comes to the United States.
If they intend to marry in the United States, the U.S. citizen may bring the fiancée into the nation with a fiancée (K1) visa. The marriage is to occur within 90 days of her entry, and she may petition to adjust her status to become a legal permanent resident (LPR) after she marries, while remaining in the U.S.
If they marry overseas, the spouse may petition to adjust her status through consular processing. Once that process is complete she would receive a Green Card at the U.S. consulate in her country of origin, and will enter the U.S. as a LPR. She can also consider seeking a K3 visa.
If she is already in the U.S., they may marry and petition to adjust her status based upon marriage, but that may be complicated by the nature of her visa, whether she entered lawfully or overstayed, and other factors -- she should discuss the details with an immigration lawyer.
When a fiancée is not in the United States, in most cases the fastest means of accomplishing immigration is the fiancée visa.

