The only way to reach La Désirade is by ferry from Saint-François on the eastern tip of Grande-Terre. The crossing takes about 45 minutes and several departures run daily in both directions. Saint-François is about 60km east of Pointe-à-Pitre, reachable by road from anywhere on Grande-Terre. There is no airport on La Désirade and no plans for one — the ferry and the island's consequent unhurriedness are part of the same deal.
The crossing runs through open water exposed to the Atlantic trade winds and can be rough when swells are up, particularly in the afternoon when the wind strengthens. If you are prone to seasickness, take precautions before boarding or aim for an early morning departure when conditions tend to be calmer. The ferry docks at Grande-Anse, the main settlement, and everything on the island is walkable or cycleable from there.
Check current schedules locally or at the ferry terminal in Saint-François — timetables vary seasonally and sailings can be adjusted for weather.