By Train
Padova is both on the Venice-Milano and on the Venice-Rome railways, many trains are available. Note that for regional trains it is mandatory to validate the ticket before boarding by using the (yellow or green) machines located on the platforms and throughout the station. You can find train connections from the following websites:
By Plane
The closest airport is the Venice "Marco Polo, which is conveniently linked with all major European airports.
Reaching Padova from Marco-Polo airport
Marco-Polo airport is well connected (45 minutes) by bus to Padova (stop "Padova Autostazione"). The bus schedule is available here. The bus heading to Padova leaves from stop I (large i) which can be reached by exiting the airport and walking towards the left. The ticket (13 Euro) can be bought at an automatic machine by the bus stop, or in cash (with the exact amount) from the bus driver, or via credit card with the busitalia veneto App (registration is required).
Alternatively, you can commute from Padova to Marco Polo airport using a shuttle service which should be reserved in advance. https://www.airservicepadova.it/en/services/airport-shuttle/
Alternative airports
Some low-cost companies fly to the close Venice-Treviso airport. A convenient alternative might be flying to the Verona airport, which is connected to the Verona Porta Nuova railway station by a bus service. Padova can then be reached by train (approximately 50 minutes). A last possibility might be flying to Bologna airport, which is connected to Bologna Centrale railways station by a bus service. Padova can then be reached by train (approximately 1 hour).