Andros is reached by ferry from Rafina, the port east of Athens (not from Piraeus). The crossing takes about 2 hours on the fast ferry, and services run several times daily in summer, less frequently out of season. Rafina is connected to Athens by bus and is about 30 minutes from Athens airport, making a direct connection from the airport to Andros reasonably straightforward. There is no airport on Andros.
From Andros, onward connections run to Tinos and Mykonos.