I made the same mistake a couple of times and would like to warn you not to do it: Don’t try buying your international train ticket at Keleti train station. You usually wait there for hours. Today there were 103 (hundred and three) travellers in front of me in the line. Unbelievable.
If you are already at Keleti, take the trolley bus no. 76 till Ferdinánd híd (Izabella utca) (7th stops) then take a short walk to Nyugati train station.
At Nyugati there is usually hardly anyone waiting at the international ticket office.
About the authors: Virág and János
Virág, a native of Budapest, and János, who’s been living in the city since 1997 are real fans of the capital of Hungary and try to awake the enthusiasm of others. They are dedicated to helping tourists to make most out of their stay.
Here you can read more about them: http://katonaapartments.hu/