No need to take expensive taxis! You can reach city centre from Budapest T2 international airport. It takes about 1 hr. You have to use bus+metro to reach city centre. Be sure to buy the tickets for the bus and metro.
In the airport look for blue bus 200E right on the departure terminal. Take that bus and it arrives to Kobanya Kispest, which is the place where it connects to metro M3 blue line. The metro is not underground just like a normal train station here. From here direct to Deak Frenc ter, which is the main city centre and this place is the connection point for all other metro lines, M1 orange, M2 Red.
oh, where to buy a ticket for the bus? Quite often the ticket machine outside airport may not work but you can buy BKV bus ticket from a shop inside the terminal near the exit gate. Cost is 300 fortint or something. keep the change ready.
It is the cheapest way to reach city centre and usually taxis charge about 20 euros or 5000 forints.