There is one   airports on Fuerteventura. The airport operator is Aena.  Information is available from their web site.  Click here for  flights-on line
 

Fuerteventura has a public transport system with many routes. www.tiadhe.com  web site has the time tables.

Car hire is also widely available.

 If you need aTaxi, agree on a price before the start.

An alternative is to book transfer together with your hotel. This service is offered by www.alpharooms.com . An other possibility is shuttledirect.com
 

If you are planning to use public transport, the trick is to ask the tourist office at your destination. To find their address & Tel. or e/mail, use the official tourist web site for Spain: www.spain.info    Look in section for destinations, or use their search.