Since last year registration of foreigners is only possible with a reservation. This reservation has to be made online at the subsequent link:
https://www.hikorea.go.kr/pt/RsvInfoPageR_en.pt
Please read the requirements: Passport, photos, fees, etc before making your appointment. At the begin of the semester the waiting time can be up to two weeks.
The Korean alien registration card is necessary for almost all things from telephone contracts, financial transaction or travel.