You can take a Taxi from the Airport to Kapsali.
You can rent a car from the airport (and leave it there when you leave).
The boat from Neapolis “Porfyrousa” will do most days one to four trips to Kythira and sometimes Antikythira.
From Piraeus (twice a week), from Gytheio (once a week) and from Kissamos (three times a week).
From mid April to mid September, once or twice a week “Drakakis Tours” from Syntagma Square (Athens) or Pireaus.
You can use the KTEL busses to Neapoli, then take the boat to Diakofti and then use local trasport, or rent a car or a bike.