There are a ton of companies, but I was told educar were the cheapest, so therefore use them, www.educar.co.kr. I forget what I paid my first year, but I have just signed on for a second year and paid 270 bucks for the basic coverage. My car is 97 Avella for comparison.
The first year I got insurance a Korean friend helped me, but this year I got a call from a woman from the company with immaculate English so was able to renew without any help. So if you wanted to try and do it yourself you could try ringing them and asking for an English speaker. Number is 1566-3000
Other companies include Samsungs Anycar, Hi-Car, AXA and Allianz searching 자동차보험 on Google or Naver will get you a ton of hits.
Calculation seems to be based on the value of your car(not the price you bought it for) and your age. I know a poor old Korean friend of mine who drives a Carenz and is 23 and he is paying nearly 2000 bucks a year!