Most hotels provide Internet and e-mail access for guests at the front desk, if not right in the room, and you can easily connect your laptop to the Wi-Fi that is common. If you have a Wi-Fi-equipped laptop, there are hot spots at the port area, the Guanahani, and in the parking lot of the Oasis Shopping Center in Lorient; service is provided by Antilles Référencement, an excellent computer shop that can set you up with a temporary Internet account or provide other computer support.
Mail is slow. Correspondence between the United States and the island can take up to three weeks to arrive. The main post office is in Gustavia; in season it's open daily 7:30-3, (except for Wednesday and Saturday, when it closes at noon), but smaller post offices are in St-Jean and Lorient. These are open a few hours each morning. When writing to an establishment on St. Barths, be sure to include "French West Indies" at the end of the address. Because of the slow mail service, faxes are widely used. There are two FedEx offices in St. Jean, right near the airport.
Antilles Référencement (Oasis Shopping Centre, Lorient, 97133. 0590/52-07-22). France Télécom (Espace Neptune, St-Jean, 97133. 0590/27-67-00).
Main post office (Rue Jeanne d'Arc, Gustavia, 97133. 0590/27-62-00). Lorient post office (Lorient, 97133. 0590/27-61-35). Saint-Jean post office (Saint-Jean, 97133. 0590/27-64-02).