There are multiple options to use public transport to get to Nami Island from Seoul as detailed below.
A popular option is to get from Seoul Station to Nami Island by train. You first catch a KTX train from Seoul Station to Cheongnyangni Station, a journey of 19 minutes non stop, then change to an ITX train to Gapyeong Station, a journey of 38 minutes.
Alternatively you can first use Subway Line 7 to get to Sangbong Station, then transfer to an Intercity Bus from Sangbong Station to Gapyeong Station. The train trip is 32 minutes and the bus trip is a journey of 53 minutes.
You can then get from Gapyeong Station to Nami Island by either catching the Gapyeong City Tour Bus (see next lesson) or catch a taxi from Gapyeong to Nami Island Wharf, where you can purchase your ticket to enter Nami Island.
If you are also interested in visiting other attractions in the Gapyeong area then check out the details in our how to get around Gapyeong lesson.