My main mode of transportation was the subway. Yonsei is right across from Sinchon Station, and most of our stops run along Line 2 (aka the green line). You can use KakaoMaps, Naver, or even Google maps to figure out which line to take and which stop to get off at. It's VERY easy to get around. There are also signs and simple maps (in English) that tell you which stop is next or which stations the line will stop at along the way. They also announce it on the speaker in Korean, Japanese, and English. After a while, you'll become a pro at riding it. Make sure not to sit in the pink seats since they're for pregnant or elderly women. There is also a section for just the disabled/elderly/etc. but I've seen random people just sit in those anyway. Not many people talk on there but sometimes they do. Most people are just on their phones.
*TIP: You need a T-money card. You can refill them at machines or convenience stores but it's cash only. Anyway, just tap that card going in and going out of the subway.
The second most-used was the bus. There are stops right in front of our goshiwon and yonsei. Again, you just use your phone app and it'll tell you which bus to take, where to stop, how many minutes/seconds until the next bus arrives, and how crowded it is. It's very convenient and can sometimes be faster than the subway. I used it to get to insadong mostly.
*HOW TO RIDE BUS: When you first get on, tap your t-money card on that little device at the front. It'll charge you. Then, exit out the side door or front door (mainly side door) and make sure to tap your card AGAIN. If you don't, it'll charge you the full price of the ride.
Yonsei is also pretty close to Seoul Station (about thirty minutes away or so) where they have all the trains (including the Korea Train Express or KTX). We rarely went here and only used it to go to far away cities like Busan.
Next is Taxi. We used the KakaoTaxi app but you need your ARC to use it and we didn't get our ARC until much later. We mostly used it in Jeju since we didn't have a car. You can choose the type of taxi you need and then it'll search for drivers in the area. Usually it takes a few seconds before a driver accepts and starts heading over to you. They're normally really quiet and just pick and drop you off. We chose to pay with card at the end of the ride. It's fast, and since there were usually four of us riding in each one, it wasn't too expensive for us.
And lastly, there is just walking. I walked on average 10,000 or more steps every single day simply by walking around campus or getting dinner in Sinchon or Hongdae with my friends.