Fanø is in Denmark.
Fanø is one of the Danish Wadden Sea Islands.
You get on the island with the ferry from Esbjerg. Travel time is 12 minutes, a return ticket for adults costs 45 DKK(~6 EUR). A ticket for a small car in the tourist season costs 415 DKK(~56 EUR). Schedules available at  (select the route "Esbjerg - Fanø"). The ferry arrives at the city of Nordby.
Travelers arriving by train in Esbjerg can take the bus line #5 from the main station to the Fanø ferry port. The ride takes aprox. 10 minutes and costs 20 DKK (~3 EUR) for adults.
The most convenient way to travel on the island is by car or bicycle. There is a bus line going from Nordby to Sønderho.
The beach, the town of Nordby, the town of Sønderho.
Take the ferry, return rides are free (you have paid for it when you bought your ticket in Esbjerg).