As far as I can tell, taxi's here charge either per distance, per journey time, or both (for example, if you are stuck in traffic, the meter will still roll, even though you are not moving...and as soon as you start moving, the distance meter kicks in again). Taxi's are very very cheap in Korea, and usually the only problem is getting the driver to understand where it is you want to go to. For example, one taxi driver tried to drive me all the way to Itaewon (quite a distance from my house), because i said the place that i was looking for, "Eeeewha", slightly differently to how a native would pronounce it ("Ewha") (the whole potato or tomato pronunciation debate comes to mind). Taxi's charge a base fee of around 1400 won, regardless where you travel to, but as with most other things in Korea, you do not have to tip. It is not unheard of for taxi drivers to charge foreigners more than the locals, since we often do not know what the correct fee should be.
You may also find that taxi drivers are very very grumpy here quite often... it almost feels sometimes like they actually had something better to do than drive you around, and actually is doing you a huge favour. On the other hand, there are some very friend and helpful drivers too..
It is always a good idea to have something with your flat and school address written in Korean on you at all times.