To get a motorcyclist's license, you need to apply for written and driving tests at an authorized institute. What you need for an application is your 1. Passport 2. Alien registration card 3. A fee of 11,000 won.
If you are wishing to drive a motorcycle 125cc or less you need only apply for a regular drivers license. Higher CC motorcycles require a different license. Contact your nearest Drivers facility for more information.