The journey from Seoul Station to Busan, the 2nd largest metropolis in Seoul, takes 2.5 hours. A return ticket costs around 100,000 KRW and a 3-day rail pass costs 84,600 KRW. So it is more economical to buy the rail pass. 

Once you have buy the ticket, you can proceed to the train gate where all the trains are docked. 

Before making your way downstairs, you should see the board for the KTX number, don't worry, they will display the information in both Korean and English. KTX departs from Seoul Station to Busan Station pretty frequently.

This is how the KTX looks like from outside. 

The inside of the KTX looks pretty cozy just like the High Speed Rail in Taiwan or Shinkansen in Japan. I guess that's the reason why the ticket is kinda pricey. 

If you have time to explore Seoul Station before your trip to Busan, you should walk around outside Seoul Station because there are a lot of things to see outside.