There are three train stations in Budapest: Déli, Keleti and Nyugati.
Most trains to Tokaj leave from Keleti train station, and a few from Nyugati. Make sure to choose a train that is marked IC (intercity).
To travel from one train station to another the easiest way is to take the metro. You can buy a ticket costing HUF 350 at a newspaper stand or from a machine. Even if you travel on 2 different metro lines, you can use the same ticket provided that you change underground.
There are four metro lines in Budapest, each one with a different colour. Click here for the Metro Railway Network map of Budapest.
Travelling to Tokaj by train
Travelling to Tokaj by Crescendo Bus