You might be eligible for tax exemption based on your citizenship (everyone except those from Canada or Ireland). You will need to submit your residency certificate to your school's financial office. They must then use that to register you as officially tax exempt with the district tax office (depending on where your school is located). DO NOT assume that tax exemption is automatic based on your nationality!
Until then, you may be subject to continued taxation. If you know that you will not be receiving your residency certificate for some time, it is strongly suggested that you opt to be taxed in the meantime. You may be able to get a refund for what taxes you paid while waiting for your residency certificate (have your financial administrator work it out with the tax office). The worst case scenario is asking your school to not tax you while you wait for your residency certificate, and having to pay all of the accumulated taxes as one lump sum if for some reason your residency certificate does not come through. But this really depends on the tax office and what they will allow.
While the actual filing of taxes is handled by your school, we cannot stress enough that applying for tax exemption is solely your responsibility. It is up to you to apply, receive, and submit your residency certificate to your school. It is also up to you to request a pay slip to make sure that taxes are indeed, not being taken out of your income. You may ask your co-teacher and/or financial administrator for any help along the process, but ultimately it is your money and your responsibility.
Understand that you or your school needs to take your residency certificate to the school's local tax office to register you as tax exempt in order for it to take effect (simply showing your school your residency certificate is not the entire process). Although your residency certificate is valid for 2 years, there is the possibility that the tax office will only register you tax exempt for one, due to your contract period and visa validity only being one year. If that is the case, you will need to go back to re-register for your second year of tax exemption. They will accept a copy of the residency certificate. Therefore it is vital that you keep multiple copies of your residency certificate on hand. If your school is not clear on the process of registering you for tax exemption, please ask your co-teacher and financial administrator to check the NET Program Guidebook(원어민 영어보조교사 관리 및 활용 길라잡이) available on the official DMOE website. In the most recent edition, the information that they need is under the "administrative matters" section (행정관리).
If you require paperwork to submit to your tax agency back home, it is best to ask your financial officer to provide you with a copy of your latest "원천징수영수증." This document is only available after your taxes have been processed by the Korean tax agency, so it may not be available until well into March or April. This document lists out your income, taxes paid, etc for the fiscal year.
Click here for more information on residency certificates.
If you are currently subject to income tax, you may want to consider signing up for "Cash Receipts." This is basically a way to keep a log of all of the cash purchases that you make during the fiscal year. While we can't explain the exact calculations, we do know that your total cash purchases for the year are factored in when calculating your income tax during the adjustment period at the end of the year (purchases on your Korean debit/credit card are automatically reported through the link to your RC number). Basically what happens is you're given a card that is linked to your RC number and phone number. Every time you make a cash purchase, you can also have them swipe the card and it will log in your cash purchase. If you don't have the card on you, you can give them your phone number. This will only work after you've signed up for the service. To sign up, please visit their website (you may want to enlist the help of your co-teacher or a Korean friend to help you navigate the site, as it's all in Korean).
https://www.hometax.go.kr/websquare/websquare.html?w2xPath=/ui/pp/index.xml
National Tax Service Website (English):
https://www.nts.go.kr/english/main.do
National Tax Service Phone Line (English Service Available):
1588-0560