There are many state programs to support foreign students. For example, a Korean Global Scholarship will allow you to study for free at Master's and PhD level, as well as get training in science and Korean for up to 6-12 months.
The grant covers tuition expenses (₩800,000), research work (up to ₩480,000), and life insurance. Students receive money to purchase books once a year.
Moreover, scholarship receivers are rewarded for their success. The size of your payment depends on your performance, and can be from 30-100% of your tuition costs. You can find more information on university websites.
Candidates can also receive scholarships from universities, private funds, and large companies.