Train
Padova is both on the Venice-Milano and on the Venice-Rome railways, many trains are available (see http://www.trenitalia.com/tcom-en).
Plane
The nearest airport is the Venice Airport Marco Polo (see http://www.veniceairport.it/), 40 kilometers east of Padova; it is conveniently linked with all major European airports. Some low-cost companies fly to the close Treviso Airport Canova (see http://www.trevisoairport.it/).
Venice Airport connections
AirService (only from Venice Airport): link
Bus: link
Treviso Airport connections
Bus: link