It's worth shopping around a bit before deciding on where to go for instruction, since both prices and the quality of training vary considerably around the island.
Both PADI (Professional Association of Diving Instructors) and NAUI (National Association of Underwater Instructors) courses are widely available. Most shops offer one or the other, but a few have personnel who are qualified to teach both. In addition to the basic open-water courses, you can often take so-called "specialty" courses such as Night Diving, Rescue Diving,and Underwater Photography. You can qualify all the way up to Instructor level locally, with at least three shops offering PADI 5-Star IDC (Instructor Development Courses).
For first-time divers, some shops feature free introductory lessons in the hotel pool or inexpensive one-day "resort courses" (usually a pool dive followed by two more in the sea).