According to Sotavento-beach statistics, windiest month in Fuerteventura is July, but with the NE trade winds blowing any time between May and September is a good time to visit the island. There is a 1-2 knot current from north to south on both east and west coasts of the islands, which is a drag since it runs in the same direction as the wind. You'll spend a lot of time going up wind. The best - and most popular - windsurfing spots on Fuerteventura are Sotavento and Corralejo.
The Sotavento/Jandia beach is almost 20 kilometers long and has many accessible spots. The most northerly one (Los Gorriones) with the F2 Surf Centre is the beach where the island's World Cup event is held every year. Wind blows most often cross/off-shore and even though the water is usually flat or choppy this beach is not meant for novices. There is no rescue service. About two kilometers south of Los Gorriones is Risco del Paso. Again, flat water and good winds. In July/August every year this beach holds a speed course.
Corralejo is the most popular tourist spot of Fuerteventura. It has two excellent windsurfing beaches: Flag Beach and Glass Beach. Flag Beach offers flat water sailing, sometimes waves up to one meter and has a Fanatic centre. It often doesn't get windy until noon but if you need a parking space you'd better get there early. Glass Beach has a rocky launch and a shallow shore. There is a good swell which breaks on the reef. If you fall down by the reef you can just keep your feet up and relax as the current will take you down to sandy flat water.
If Corralejo gets crowded try Cotillo on the west coast for waves (strong current and huge waves, up to about 4 meters). Sotavento has lots of room and is the best spot for flat water.