Coming to Korea from a rural area in the USA which has no public transportation (as in, no bus, train, taxi or even uber), I was nervous to learn how to use public transportation for the first time in my life, alone and in another language! As things turned out, however, I was pleasantly surprised that the process of navigating public transit was fairly easy, and I am now really comfortable with the process.
Most Koreans have cars, which they will drive from place to place. I had the opportunity to get an International Drivers License in order to be able to drive in Korea, but honestly, the drivers here terrify me, so I am glad I did not make this decision. Drivers here are crazy! I feel much safer on the public transportation system than I do out on the rods in Seoul. Luckily, public transportation is plentiful, even in small towns in Korea. Even in the tiniest of towns, there is a bus that can take you to a larger town, and there are (extremely cheap) taxis everywhere, too. To give you some idea of the cost, most of my taxi rides under 20 minutes cost no more than 7000 won (about 6 dollars). You can also take trains in larger cities and in Seoul, and it is very easy to use the subway and bus system in these places.