Fortunately it takes only 1 minute to add Korean Keyboard input method in Windows 8. Here you will find a video tutorial and a full description to achieve it.
If you are on Windows 7 please check How to type Korean on Windows 7?
This tutorial is is divided in 2 parts:
1. Video tutorial
2. Tutorial with printscreens
1. Video tutorial
2. Tutorial with printscreens
Click on the printscreens to get fullsize pictures.First you have to put your mouse to the top right corner. When you do that a black bar appears (called the "Charm bar").
1. Just click on the search icon from this bar:
2. Type "input method" in the search box and choose "Parameters" in the list of places to search.
Then click on the result that appears on the left "Modify input methods":
3. A "Language" Window should pop up. Click on "Add a language":
4. Find Korean in the list and click on the "Add" button at the bottom:
5. Now you can switch to Korean by clicking on the language switcher. It should be on the right in the taskbar:
Now you can type Korean!
Check here (part 3) if you want to get information about the Korean keyboard layout.