Ditto the minibus idea, it runs until the last flight has landed, and its pretty straightforward door to door service. The taxi company that owns the rights to sit curbside at Ferihegy is OK: They're fine guys, they just charge too much. The regular cab services sit a ways away from the terminal and you have to call their dispatch to order one. City Taxi is reliable, they're number is 211-1111 (from a mobile add 06-1 before). Should be about US$15-20 (Ft3000-4000) to the city center that time of night.
have fun!