The journey from the Athens airport to Lavrio, the ferry port takes approximately 30', allow 45' in order to stop and collect the ferry tickets at the booth by the port. Ferry schedules are published quite late but the best website to look for the sailing times is www.openseas.gr. In high summer booking for a car is recommended.
When you arrive at the port of Korisia in Kea, someone will be there to accompany you to the house.
A car can be rented from the airport (recommended) or on the island.