From Venice. There are many options to get to Pauda from the Venice airport.
From Treviso. You can either go to the main Treviso train station or go to the train station of Venice and from there get a train to Padua.
From Verona. Get a bus to Verona train station and from there a train to Padua.
From Bologna. Get a bus to the train station and then a train to Padua.
A shuttle service is available for all the airport listed above (Air Service Padova).
There are also many other international flights to
You can find the travel information here or here.
Please check the official page of the city of Padua to have information about parking in the city.