There are so many ways to go to Nami Island but it really depends on how cheap or how comfortable you want your trip to be.
On average..I prefer to ride ITX-Cheongchun line and buying the ticket to secure a numbered seat is easily done online.
You could ride ITX-Cheongchun to Gapyeong station either from Yongsan Station or Cheonggyanni Station.
On a side note..Cheonggyanni Station is the filming location for the Korean drama Secret Garden; where Joo Won (Hyun Bin) was the president of LOEL department store. It's actually LOTTE department store.
How to purchase ITX-Cheongchun ticket online?
First, go to KORAIL website: http://www.korail.com/ and choose English. ^^
Click "Booking" and then "Book Online".
Fill up the date, your desired stations, choose "ITX-Cheongchun" line and number
of guests. After that press next button.
Select the time of departure and press next button.
Fill up your details and press next button.
Confirm your details and fill up your payment information. After pressing next
button you will be prompted with booking confirmation.
Print the booking confirmation and bring it together with your passport to the train where you will depart from. Eg. If you depart from Cheonggyanni Station, bring the booking confirmation and passport to the ticket officer and exchange for the actual ticket. *In my case, I just showed them my passport and that was it*
It takes roughly 40 minutes from Cheonggyanni Station (4,000won) and 55 minutes from Yongsan Station (4,800 won) to Gapyeong Station.
My experience riding ITX-Cheongchun line is here.