First, a little background on U.S. immigration law. Marriage to a U.S. citizen or lawful permanent resident provides foreign-born persons a direct path to U.S. immigration. Contrary to popular rumor, however, they do not immediately or automatically receive green cards or U.S. citizenship.
If you are a U.S. citizen, your new spouse becomes your "immediate relative," and may receive a green card as soon as the two of you successfully complete the application process. This can take several months.
If you are not yet married and your fiance is still in Haiti, you can, if you are a U.S. citizen, petition for him or her to enter the U.S. as a fiancé in order to get married in the United States. After the wedding, your new spouse can apply for a green card, if desired. You can also choose to get married first in Haiti or another country, and then apply for an immigrant visa with which to enter the U.S.– the equivalent of a green card.
If you are a lawful permanent resident, your foreign-born spouse is considered a "preference relative," in category 2A of the visa preference system. ,Your spouse can complete the process of applying for a green card (and enter the U.S.) only after a visa number has become available. Annual limits on the number of visas given out in category 2A create years-long waits. The application process itself adds more months to the process. U.S. permanent residents cannot petition for fiancés.