Paros can be easily reached from Piraeus, where there are daily ferries going to the Cycladic islands. The journey takes three hours or more depending on the speed of the boat you take and the schedule it follows.
Sometimes there are ferries from Rafina to the island of Paros. On the airport of Athens there are regulair busses going to Rafina, and you don't have to drive through Athens itself. Off course you can also take a taxi. The ride takes about half an hour. It's also possible to fly to the island of Paros from Athens.
If you want to check the ferries from and to Paros and order a ticket - click here.
Paros has an airport for for domestic flights and can also be reached by plane from Athens (national flights only because there is no international airport).