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.
Apparently you could sleep from €25,- per night and up, The official web of the Canary Islands  has a nice system for locating hotels and offers in Fuerteventura.
Atalaya de la Rosa del Taro, ☎ +34 928 175 10, . Is in a quiet inland area 13 km from the capital It's 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, a bathroom and a terrace with panoramic views. The house is situated , far away from the tourist resorts, but very well linked. The nearest beach is ten minutes drive away
Casa de la Burra, ☎ +34 928 175 014 (firstname.lastname@example.org), . Isolated of the urban centers, this small but welcoming house for two persons are a green retreat with solar energy for the sanitary hot water and biological purification of residual waters used for watering. *Fraggle Roca, 53 Castillo Mar (Opposite the San Jorge hotel), ☎ +34 928 160 117, . 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.
Oasis Jandia Golf, Barranco de Vinamar, La Mancha, Jandia, 35625, ☎ +34 928 546 550 (email@example.com), . Right on a 18 hole golf course, and good views 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 quiet 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