Buses. Inter city buses are cheap, convenient, reliable and comfortable. There are several a day between most cities. The interchanges are generally in, or close to, the city centre and walking distance to hotels and hostels.
Trains are more expensive and sometimes slower than the bus. Coverage is limited. The high speed KTX train between Busan, Singyeonju (connected by local bus to central Gyeongju) and Seoul is comparable to the Japanese Shinkansen and the French TGV.
Local buses (and taxis) can generally be picked up at the terminal.
Bus and train terminals usually have a tourist information centre attached, or nearby.
Taxi drivers in Seoul have a bad reputation for ripping off tourists, sometimes for astronomical sums according to anecdotal evidence. But rip offs are not routine, as they are in some countries, and the authorities are trying to clamp down on the dishonest drivers. There are apparently rewards for reporting any bad experiences.
Need to book tickets in advance?
No. Except perhaps in the busiest holiday periods.
Sometimes by ticketing staff (although you only need to be able to say, or point to, the name of the destination). Rarely by drivers.
The origin, destination, platform and (where allocated) seat number will be printed in English on the ticket for inter city buses. Destination boards are usually in Korean and English. Local buses in popular cities often have bilingual announcements.
Make the most of the tourist information centres. The staff almost always speak some – and sometimes excellent – English and they generally have a stock of English language city maps and local bus timetables and will write notes in Korean to show the bus or taxi driver to get to your hotel or hostel.