Your best bet to get to Paros:
fly into Athens, take a taxi, the metro or the airport bus to the port of Piraeus and catch one of the boats listed in the ferry schedule

Other options depend on the season and are subject to change:
- catch a flight from Athens Airport to Paros
- check out rumours concerning international flights to Paros
- fly to Myconos or Santorini (Thira) and catch a boat from there to Paros
- catch a boat from Rafina (closer to Athens Airport than Piraeus) or Lavrio (less travel time to Paros)

So far Paros Airport only serves domestic flights.
Olympic Air >>
Aegean Airlines >>
Sky Express >>

Online Schedule of Greek Ferries >>