If you're just so lazy to figure out how to get to this island by taking subways, I would suggest you to purchase a package from an agency near Insadong. They charged me around 23,000 won for a day trip to Nami Island, including 2-way bus fares (Insadong-jetty), boat ride and entrance visa to the island.
We were day during summer. It was still beautiful, but less. It didn't look as amazing as that during other seasons. The island wasn't so big, but still got tired if walked around. So we rented a bike for a half hour to wander around.
There was one ice-cream stall right beside the bike-renting counter. The ice-cream was superb nice! Worth a try! Don't put too much expectation on the food sold over there. They were pricey and not delicious at all. But we had no choice, we were at the island!