Many ways lead to Fourni, all of them across the water. Your only chance to get a helicopter ride is to fall in need of a hospital. Several times a week the Piraeus-Samos car-ferries go to Fourni. However, their timetables do not depend on flight schedules at the airport of Athen or Samos, so plan to stay for a night or two.

Time schedules
http://www.aferry.co.uk/fourni-ferry.htm
http://www.gtp.gr/
http://www.openseas.gr/OPENSEAS/index_en.vm
http://www.greekferries.gr/

Port Police Fourni
Phone: 0030-22750-51207

Port Police Samos
Phone: 0030-22750-27318