If you cannot fly directly to Venice, look for a connecting flight reaching Venezia from Rome or some other convenient European airport, like e.g. London Heathrow, Frankfurt am Main or Paris Charles De Gaulle.
The best way to go to Padova from Venezia airport is by bus. You have to take a SITA company bus (those are the blue buses). Tickets can be purchased in the Arrivals Hall, at the ATVO booth (cost 3.15 euros). The tickets can also be bought on board the bus, but then they will cost 4.18 euros. Exit the Arrivals Hall and turn right. At the rigthmost stop you'll see a blue SITA sign. Board the blue SITA bus to Padova. The first stop is Venice. You must get off at the bus station in Padova. The timetable can be found here. The trip lasts one hour. Note that there is no taxi rank in the bus station in padova. You have to walk to the railway station and wait for a taxi on the taxi rank The walk from the bus station to the railway station is a short one (5 minutes) but not particulalry fascinating, and you have to consider the luggage as well.
You can also take a bus to Mestre and there take a train to Padova. This has the advantage of leaving you at the railway station, from which you can directly take a taxi. From Venezia airport you have to take an ACTV bus (those are the orange buses). The lines that go to Mestre are the 5 and 15. Note that the tickets have to be bought before you get on board, you can buy them at the newspaper agent inside the airport. The winter timetable of the ACTV company is not out yet, of course, but these buses are usually rather frequent. Ask the conductor to tell you when to get off (you have to say you want to go to "la stazione di Mestre"). All the trains going from Venezia Mestre to Milano, Bologna or Roma, plus several local trains, stop in Padova (the ride time is 20/30 minutes), many trains are available. If there are long queues in front of the counters, remember that you can also buy the ticket at the automatic machines just in front of the counters. Both at the counters and at the automatic machines you can pay with any internationally valid ATM card (i.e Cirrus, Maestro etc.). Remember to stamp the ticket in any yellow machine inside the station before getting on the train, otherwise you get a fee. Note that for Eurostar (ES) trains you need to pay a hefty supplement. A lower supplement is due for the Intercity trains (IC).
From Venice Marco Polo Airport you can also reach Padova by a shuttle service. That is more expensive, but will leave you exactly at your hotel. You can choose two different companies (reserve a seat at least 24 hours in advance!):
there is also an on-line reservation form
Fare: 20.66 euros per person (fixed price)
Fare: at most 25 euros (the price can be lower, depending on the number of people travelling)
Both companies offer the same service: someone will wait for you at the airport with a sign. Then you will be taken to Padova on a small van. The ride lasts aproximately 40 minutes.
Finally, it is not advised to take a taxi and go directly to Padova, as it may turn out to be quite expensive (aproximately 75 euros).
First and second class are available; for Eurostars and Intercity trains a supplement is required, and in some cases a seat reservation is mandatory: so, specify which train you are going to board when asking for a ticket.
All tickets (both round-trip and one way) have a validity of 2 months. Before boarding the train, you have to validate them by stamping them in the yellow machines located on the platforms and throughout the station.
You can find timetables and more detailed information at the Italian Railway Webpages (Ferrovie Italiane).
In Italy highways require a toll. You pay it when you leave the highway; a ticket automatically issued to the driver when entering the highway is required for payment. You can use most major credit cards in automatic machines in the lanes marked: "FastPay" or "Viacard".
If you are not familiar with the competitive European (and, in particular, Italian) way of driving, avoid long travels by car; it is quite different to travel 200 or 300 miles in Italy or in the United States, and in particular it is difficult to estimate the required time.
Car rental fees depend on the car type and the length of the rental period; and may increase if the car is returned to a different location. The lowest fee is of 50 euros per day; inquire locally at your favorite international car rental company for more information. Car rentals available at Venezia airport are: Hertz,Thrifty, Avis, Maggiore, Europcar, Sixt.
If you are going to come by car, make sure that your hotel has a parking lot, as parking in the centre of Padua might be quite dificult.