If you have a computer with Windows 8 (I have Windows 7), it’s a bit more difficult to change your keyboard’s input. This article helps explain what changed between Windows 7 and Windows 8 and guides you to the screen where you can change your keyboard’s input language by adding Korean and other languages to its repertoire.
NOTE: A comment on the article says that pressing Win + X opens the “Power user shortcut menu (Device Manager, Control Panel, Command Prompt etc.) and then you can select Control Panel from it”. Another comment explains that rather than clicking on all the different options in Control Panel, put “language” into the Control Panel Search, then go from there.
The “from there” should entail clicking on Add an input method to access the list of other keyboard input languages. Remember to add both Korean and Korean IME.