When departing Budapest by air (and presumably when arriving too), don't bother with the various taxi/minibus services. The public transport alternative is efficient, perfectly easy to use and far, far cheaper (about £1 each way, as opposed to £6ish for the shuttle service).

From the town centre (Deak Ter) to the airport, simply take the blue metro line to the end of the line, then jump onto the clearly signposted no: 200 bus (complete with little aeroplane logo and English announcements). It goes to Terminal 1 first, then Terminal 2, and the entire journey to Terminal 1 takes about half an hour.

You need to validate one single ticket on the metro, and then another on the bus (or vice versa if arriving). True, ticket staff don't speak much English, but they are quite keen to help, and "2 single tickets" is widely understood (if various options are proffered, single tickets are the little flimsy orange ones with perforations).

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