Airport Shuttle Minibus: 

http://budapest.airport-shuttle.com 
http://www.airportshuttles.com/budapest.php 

Take a taxi: taxi info 
Mostly taxi drivers speak English, but first you should register just there when you leave airport building. You will find a small taxi registration hut, they will ask the exact full address of the hotel. It is very safe.

Public transport:

http://www.bkv.hu/en/