There are flight and ferries to Paros from Athens airport or from Pireaus airport. You could also come by ferry from a nearby island e.g. Naxos. As far as concerns the transportation once you get to Paros, you could get around by public bus which is cheap and runs frequent itineraries. You pay for the ticket once aboard the bus. Time tables are provided from the bus stations at Naoussa and Parikia. If you would like to stop a bus to get in just wave, to get out tell the driver. Bus ticket cost around 1 euro.
There is also an option of renting a motorcycle, prices start from 10 euro per day and going upwards. We strongly reccomment to drive only of you have a licence, rentals will not ask for one but the police will and if you become involved in an accident there will be trouble. There is also the option to rent a car which is around 25 euro per day for a small car and upwards depending on the car model. Always have a driving license. There are options of Boat taxi in the port which is cheap but avoid it if its windy or you have sea sickness. If you prefer a taxi just wave, fairs are cheap but the taxi driver takes different people to the same ride. There are also tours of the island provided by travel agencies and it is a convenient way to see it all.