Here's a plan of Keleti station.

The Railjets invariably arrive at one of the bay platforms, numbered 10-13.

The best bet is to exit the station through the small exit just below the platform 13 buffers. Then walk along the side of the station to the "main" side entrance, where it says "taxis". There will be taxis of various companies there, but I don't recommend taking one - it's a lottery. I recommend to call City Taxi (2111111 on any local network a mobile phone connects to, or 06 1 2111111 is the landline). Tell them you are standing by the Kerepesi (pronounced roughly: Kerra-peshee) street entrance to the station. They are used to non-Hungarian speakers and will give the necessary details of the pick-up.

Also, beware of other outfits with similar names trying to cash in on City Taxi's reputation. I think there is one company called City Park Taxis or similar, for example.