I found what I believe is the best deal on a SIM card in Korea. I have been using it for about 6 months now and I still think it is fantastic.
I use EG Sim Card (egsimcard.co.kr). I personally think it is the cheapest and best service offered. You don’t have to deal with the hassle of paying for a prepaid phone, or starting a contract at a company that will later have cancellation fees.
I paid 10,000 won, $10, for it online about a week before I arrived in Korea. I had it delivered to my friends house, where it was delivered in less than 48 hours.
Before I left America I made sure my Samsung Galaxy S3 was unlocked for international travel (IMPORTANT! Do not forget to do this or the Sim card will NOT work).
As soon as I arrived I put I switched SIM cards, changed my APN settings ( use this blog to change APN settings http://koreasimblog.blogspot.kr/2013/04/guide-to-setting-up-setting-up-internet.html ), then I could use my phone no problem!!
The Sim card comes with a phone number for you to use, and I pay about about $20 a month to pay for data and voice. You are getting data from one of the big service provider companies, KT. So the 3G speed is pretty good.
The EG SIM CARD facebook page is also fantastic. I have gone there and posted several questions, and I have gotten a response to my post usually within 24-48 hours. Their customer service is just fantastic. (https://www.facebook.com/egsimcard)
You can also download the app to help you easily check your balance, update your account, and top up voice and data. On the app, or website, you can pay with global credit card.