There is no airport on Spetses island. The International Airport of Athens is the closest to Spetses island and it receives flights from all Greek islands and from all the world.
From the port of Piraeus in Athens, there is several ferries to Spetses every day. The trip from Piraeus to Spetses by ferry (hydrofoil) is 2 hours.
From the airport of Athens, you can organize your Athens airport transfer online to Piraeus port.