Antwerp has its own airport, but it's much more likely you'll be flying into Brussels (Belgium's main international airport), Charleroi (for budget flights within Europe) or Amsterdam and then continuing by train.
Budget flights to Antwerp
Prices to/from Prague range between 48 and 127 Euros. Thanks to the diamond industry, you might find good deals on flights to Africa as well.
Getting from the airport to the city centre or hostels
Busses 14 and 16 will take you to Centraal Station in the city centre. The closest hostel to the airport is the International Youth Hotel. To go here get off the bus at Van Den Nestlei.
A little bit further is the Boomerang hostel. Get off at Belgielei.
For Den Heksenketel hostel, take the bus to the last stop, go into the metro (station Diamant), take any tram to Linkeroever and get off at Groenplaats. This will take about half an hour.
If you're staying at the HI hostel (Op Sinjoorke), take tram 2 (direction Hoboken) from the same metro station and get off at Antwerp Expo. This should take you about 45 minutes.
When you get on the bus, buy a ticket from the driver (1 Euro). When you change to another bus or tram within the hour, you don't need to buy another ticket, just punch your ticket again.
Budget flights to other cities in Belgium
BMI Baby flies between Brussels and Dublin, Cork, London, Leeds, Manchester, Nottingham, Belfast, Glasgow, Edinburgh, Aberdeen, Durham, Inverness, Stornoway, Nice, Madrid, Palma de Mallorca, Oslo, Stavanger, Stockholm and Gothenburg.
Virgin Express flies between Brussels and Nice, Madrid, Barcelona, Valencia, Malaga, Palma de Mallorca, Lissabon, Faro, Geneve, Copenhagen, Rome, Milan and Athens.
RyanAir flies between Charleroi and Dublin, Shannon, Glasgow, Carcassonne, Barcelona, Valladolid, Stockholm, Rome, Milan, Pisa and Venice.
Atlas-blue flies between Brussels and Marrakech and Agadir.
Vueling flies between Brussels and Barcelona and Valencia.
WizzAir flies between Charleroi and Warsaw and Budapest.
Aer Lingus flies between Brussels and Dublin.
Maersk Air flies between Brussels and Copenhagen.
Blue1 flies between Brussels and Helsinki.
Corendon flies between Brussels and Istanbul.
Getting to Antwerp
From Brussels, take the train to Brussel Zuid/Bruxelles Midi and get off at Brussel Noord/Bruxelles Nord, the first stop. Change to an IC train to Antwerp or Amsterdam there. A ticket costs 6,20 Euros. It will take about an hour.
From Charleroi, take bus A to the train station. On weekdays there are 2 trains to Antwerp an hour, which take an hour and a half to get here. In the weekend however there's only 1 train an hour, and it takes over 2 hours! You can buy a bulk ticket at the Airport Ticket desk in Charleroi for 10 Euros, which is valid for both the bus and the train.
If you plan to do more rail travel in Belgium, you can buy a GoPass (if you're under 26) or a RailPass (if you're not), which costs 43/65 Euros for 10 rides within a year, and can be used by more than one person. If you're over 65 you can travel anywhere (and back) for 3 Euros a day (except on weekdays before 9.01). Children under 12 travel for free (with a maximum of 4 kids per adult).
Other nearby airports
Since Belgium is such a small country, you could fly into one of the neighbouring countries as well. From Rotterdam it will take about 1 hour to get to Antwerp by train, from Amsterdam (Schiphol), Eindhoven (via Breda and Roosendaal), Maastricht (via Luik/Liege and Leuven) or Lille it about 2 hours, from Paris (CDG) about 3 hours (via Brussels), from Cologne (Bonn) about 4 hours (via Cologne Hbf and Brussels).
Finding cheap flights in Antwerp
The best places to look for cheap flights in Antwerp are Airstop, Sint-Jacobsmarkt 84, open on weekdays between 10 and 17.30 , and Joker, Sint-Jacobsmarkt 40, open Monday to Saturday between 10 and 13, and Monday to Friday between 14 and 18.