First of all, you’ll need to enable Korean Keyboards in order to type in Korean.
Go to Settings > General > Keyboard > Keyboards > Add New Keyboard
Scroll down and choose “Korean”
There are two options given to you: Standard and 10 Key. Select the option you prefer. The layout of the standard option is like the typical Korean keyboard which has all the consonants and vowels. The 10 key option is similar to the numpad keyboard on PC computers.
Now you can see that Korean is added on your keyboards as below.
You can test it on an app where you can type such as Notes. There should be a Globe button in the bottom left corner. You can either: a) hold it down the icon, options appear on the screen, and select Korean - 한국어, or b) keep tapping on that Globe button until you see your Korean keyboard.