Public transportation in Korea is extensive, inexpensive and convenient. Seoul has one of the largest subway station systems in the world with instructions in Korean and English.
Also, there are two types of buses, both efficient and cheap. One is the express bus where seats have to be reserved. The other is the intercity public bus with unreserved and the cost is about 1000 won per ride. These buses run in all towns and cities around Korea.
Taxis are fast and affordable. There are two types of taxi: cheap regular cabs and luxury black cabs.
Trains are punctual, fast, clean, and safe. The train system connects Seoul to all major cities in South Korea. The cost is similar to express buses.
You might find it difficult to drive in Korea, especially in Seoul. Traffic is a common problem and the gas is expensive. You also have to get an International Driving Permit to drive a car in Korea.