From Athens you can take the bus to the South of the Peloponnese, to Neapolis or Gythion and then the ferry to Kythira. There is a daily ferry connection between Neapolis and Kythira (outside the season 6 times per week). From Gythion once a week a ferry sails to Kythira.
The busses in Athens leave from the bus station at Kifissou street 100. You can reach this bus station with Line X93 from the airport and with Line 051 from Omonia square (departure at the corner of Zinonos and Menandrou street).