If you and your husband or wife have already gotten married, and your spouse is currently in Haiti, you will start the green-card application process by filing Form I-130 with USCIS. After USCIS approves the I-130, spouses of U.S. citizens can continue on with visa processing, while spouses of permanent residents must wait (around two year, in most cases) for a visa to become available in their category.
Next, your spouse will go through consular processing for an immigrant visa. This means your spouse submits paperwork to, and attends an interview at, a U.S. consulate in Port au Prince, Haiti. (The U.S. petitioner may attend, but is not required to.)
Upon approval, your spouse enters the U.S. on an immigrant visa, at which time he or she becomes a lawful permanent resident.