The great thing about living in Seoul is that most railway stations have the same name as the subway station it is nearest too. This means that Seoul Railway Station is right next to Seoul Subway station (Seoul yuk/ 서울역 ) on lines 1 and 4. The number of this subway station is 426. If you need to take the KTX, you can catch it here. But there are also many other cheaper and hence slower trains.
The picture below show all the train routes that exists. Sometimes it’s faster to take a bus. Here is the web-site for all the trains.
There is an Old Seoul Station, but no train leave from that station anymore. Don’t worry about going to wrong one, no taxi driver will every take you there and if they did, it’s an easy 2 minute walk away from the new Seoul Railway Station.