From Milazzo (the nearest harbor to the Aeolian islands, on the north coast of Sicily): you can reach Filicudi by ferry or hydrofoil. There are several trips a day all the year around.
From Reggio Calabria and Messina: there are several hydrofoil trips a day all the year around, with some stops in the other islands.
From Napoli (change in Salina or Lipari): By ferry, with
Siremar, twice a week in the winter and up to 6 trips in the summer; by hydrofoil,
Ustica Lines, once or twice a day, only in the summer (10 June/20 Sept.), stopping in Lipari.