If you need Korea Electronic Travel Authorization (K-ETA), please go to this link. It costs between US$7 - US$8, and it is good for 3 years from the date of issue. Multiple entries to South Korea are allowed during the validity period.
There may be a separate Online Payment (Processing) Fee.
How to apply and pay
Visit the official website: Go to the official K-ETA website at www.k-eta.go.kr.
Fill out the application: Complete the online application form with your personal and travel information.
Upload documents: Upload a recent profile photo and any other required documents.
Pay the fee: Pay the 10,000 KRW (US$7 - US$8) fee online using a credit or debit card.
After submitting your K-ETA application, you should hear back within 72 hours. So it should be a fairly straightforward and quick process to apply for and obtain a K-ETA.
WARNING: Please be careful of similar agencies/phishing sites that charge high fees under the (false) pretext of providing K-ETA application agency (or expediated) services.
If you need a visa, please contact Professor Hyun Kyu Kim at Korea Institute for Advanced Study.