From airport to city centre
Public transport by train and bus:
Ferihegy 1 to Budapest: there is a train station conveniently located two minutes walk from the airport. Trains run frequently into the heart of Budapest, to the Nyugati Pálya Udvar (west railway station). It takes about 25 minutes and costs 300 HUF one way (just over 1 euro). From here, you will be able to take a tram, a bus, or the metro on to your destination.
Ferihegy 2 to Budapest: you can take the number 200 bus to terminal 1 to catch the train, or stay on the bus until it terminates at Kobanya/Kispest and take the blue M3 metro line into the city. This is more convenient if you need to get to places in the south-east of the city. The M3 journey will take you an hour.
Train ticket: 300 HUF (1 euro)
Each single ticket on other public transport: 320 HUF (just over 1 euro)
If you prefer a more private mode of transport, you can book a spot on an airport shuttle bus, which will take you to your door.
2000 HUF (7 euro) per person on the spot
1800 HUF (6 euro) if you book in advance, this is cheaper than a cab if you are on your own.
Downsides: sometimes you have to wait for a shuttle bus to fill up with people who are all going to your area. And if there are more than two of you, you might as well book a taxi.
The most expensive of the lot, of course, but by western standards it is still extremely cheap. This will be cheapest if you order a cab in advance from normaltaxi.hu.
3300 HUF (12 euro) to most places on the Pest side
3700 HUF (13.5 euro) to most places on the Buda side
500 HUF supplement to places in Budapest which are further out
Check when you make the booking where the taxi driver will be waiting. Sometimes they wait for you in the arrivals lounge, and sometimes they wait in the car at the “Rendelt Taxi” sign just outside the terminal.
If you take a taxi waiting in the rank at the airport, it will be much more expensive, and there is many a horror story of tourists being taken to the wrong address and forced to pay an extortionate fare for this “privilege”.