The easiest and fastest way to reach Ferrara is flying to Bologna airport. Indeed, this is the closest airport to the city (about 45 km), even though other solutions are possible, such as flying to Venice, Verona or Milan Bergamo airports as well.
From Bologna airport there are two ways to get to Ferrara:
1) Just outside the airport (on the left, at the bus parking) there is a shuttle bus service, called Bus&Fly, providing daily connections to Ferrara city centre, 8 times a day. You can check all the info, stops and timetable here: http://www.ferrarabusandfly.it/en/. The cost is 15€ each way but it's recommended as it takes you directly from the airport to Ferrara city centre.
2) The cheapest way takes longer, and it could be less convenient if you travel with many luggages and need to carry them all with you: just outside the aiport, on the right, you can find a bus called BLQ, providing connections from the airport to the Bologna train station, many times a day. For more info visit its website: http://aerobus.bo.it/en.
At the train station in Bologna you can then take a train to Ferrara (the final destination most of the time is going to be Venezia Santa Lucia, for the cheapest trains 'Regionali', but do not worry, they stop in Ferrara) and you can check the timetable here: http://www.trenitalia.com/tcom-en.
Hopefully these info have been useful, we wish you all a pleasant journey to Ferrara and see you soon here!