Fuerteventura is a volcanic island, in some places untouched but in others heavily developed for tourism. Note that "Fuerteventura" roughly translates to "strong winds" or Fuerte (Strong) Ventura (Venture) depending on your level of Spanish, and the island is known for its wind surfing and kite surfing.
Spanish is the national language in Fuerteventura, although English and German are widely spoken in many tourist areas.
Several ferries run from Tenerife, Grand Canaria, Puerto del Rosario, and Lanzarote. The two major lines are:
The bus lines from Puerto del Rosalio (via airport) to Correlejo, Caleta de Fuste, Morro del Jable and Cotillo are easy to handle, cheap and very reliable . It is extremely easy to get from Correlejo to the sand dune beaches south of town.
Appartently you could sleep from €25,- per night and up 
Fraggle Roca, 53 Castillo Mar (Opposite the San Jorge hotel), ☎ 0034 928 160 117, . Sea view from upstairs bedroom balcony. One bedroomed duplex. Situated in the town centre of Caleta de Fuste. Close to everything, the beaches, the restaurants, the bars. Just a quick 10 min taxi (approx 10 euros)from the Airport. Caleta is popular with families and couples, quieter than other resorts. sleeps 3 Adults or 2 adults and 2 children. Includes, twin beds, sofa bed, washingmachine, microwave, british TV, Aircon in the bedroom. Communal pool.
Atalaya de la Rosa del Taro - is situated in a very quiet area, 13 Km far from the capital-Puerto del rosario- and 10 minutes from the airport. It is a small, traditional, restored house for two or three people, sun-wind energy and recycled water, reused for the plants. It has a bedroom, a kitchen-living room with fridge and CD-radio-cassette, and a bathroom. It also has a terrace with panoramic views. The house is situated inland, far away from the tourist resorts, but very well linked. The nearest beach is ten minutes drive. You can do trekking or cycling or birds observations. Furthermore there is an engraving and pottery workshop.
Oasis Jandia Golf, Barranco de Vinamar, La Mancha, Jandia, 35625, ☎ +928 546 550 (firstname.lastname@example.org).  Situated on a 18 hole golf course, the location has excellent views of Barranco de Vinamar.
Take the air conditioned buses which run regularly up and down the island, or hire a car to really see this quite and beautiful island. Famous for its long white sandy beaches in the north and south of the island. Go into the mountains to see how the locals survived on this arid island over the centuries. And discover the strong connections with the countries of South America. Learn a few words like GuaGua (wah wah) means bus. Worth the effort to leave the resorts.
Their appears to be a lot of surfing going on.
One website mentions it is possible to get around for $40-50 
Appartently you could sleep from €25,- per night and up