I am also on an F-visa, taught at a middle school for a year and an art hagwon for 6 months. I have been doing private tutoring for elementary age for last 1.5 years, and currently have 13 students I teach each week.

I would recommend looking at facebook groups for teaching in Korea, there are about 3-4 that are good. If you come around February, there are many hagwons that offer part time teaching (no benefits) for 30-40/hour, 15-20 hours a week for f-visas. I would avoid the kids cafes, and look for something with an after school program or hagwon. I taught at an art hagwon for elementary school students for 16 hours a week, class size was 5-6 students, just helping paint something, no prep outside of class.

Also, wherever you live, make and put up flyers. Thats how I established my student base in my area. Go to the office of some apartments in your area, and pay to hang your flyers by the elevators. Do some trial classes, get some students, and just network with your students parents and grow in that area.

After you have a solid student base, you can go from there. I don’t know the details of opening a legitimate teaching business in Korea, but I do know people who make alot of money by starting their own hagwon or teaching group classes out of their home/rental space.