Our itinerary for Seoul covered 3 main areas:
1) Myeong-dong
2) Nami Island to Sokcho
3) Ewha University
The subway and train stations in Korea are very efficient and you would have no problem navigating the stations provided you know which station you have to disembark at and which exit to take - some stations can have up to 6 different exits.
I used the Korea Subway_K-ing app (I'm on Android) and it worked like a breeze. It calculates 2 different routes - one with the fastest way to get there, another, the least amount of transfers. They also have functions for point of interests but I had an existing itinerary so I didn't use it.
The longest distance we had to travel was from Myeong-dong station to Gapyeong station where you get off and take a taxi to Nami Island's ferry terminal. We headed to Sokcho after Nami Island so there's a bit of complication there.
Nami Island to Sokcho directions
From Nami Island carpark, take a taxi to the Gapyeong station then take the train to Namchuncheon train station where you disembark and take the exit that says 'to Chuncheon Bus Terminal' (if I recall correctly, it was exit 3).
Click on the map to enlarge.
At the exit you'll be taking a pedestrian bridge across the road. When you get to road level, face the station and walk towards the left down the road. You'll reach a traffic light junction where you turn left again then go straight till you see e-mart and Chuncheon Bus Terminal on your right.
At the station, buy a ticket for Sokcho (it will look like the photo above) and head to gate 5.
The signage is on the outer side so stick your head out of the building to look for it.
The bus ride will take about 1 and a half hours and you'll arrive at the Sokcho Bus Station.
Sokcho to Seorak National Park
Getting to Seorak National Park is a breeze compared to getting to the province itself.
Right outside the Sokcho bus station is the local bus stop.
The 7-1 bus to Seorak National Park has a 30 minute frequency. Get off at the last stop. Another option would be to take the 7 bus if you come across it. The last stop for the 7 bus is also Seorak National Park. Take the same bus (7 or 7-1) to get back to town.
Sokcho to Seoul
To get back to Seoul, take the bus from the Sokcho bus terminal.
The Dong Seoul bus terminal is a 2 minute walk to the Gangbyeon subway station (Line 2) so you'll be able to easily access other train stations from there.