If you are running XP go to Control Panel -> Regional and Language Options -> Language Tab (at the top). There you should check the "Install files for East Asian laguages" box. Also, go to the Details button and "Add.." the Korean keyboard for the IME system. I think that should do it. With IME installed you will either see a bar at the top of your screen or in the lower right hand corner to the left of the system tray showing what keyboard you have selected. With the Korean keyboard selected hitting the right ALT key will toggle between the English and Korean fonts so you can then type in Korean.
. Right-clicking on the IME bar will give you more display options, left-clicking letting you choose a keyboard. You can also install the Japanese keyboard there too so you can type in Japanese as well! You shouldn't need to install a language dependent operating sytem unless you are running windows 95 which you shouldn't be running anyway
. I think the instructions in the link above that Hyunwoo posted should get the fonts to display in the browser you are using.
Is this information detailed anywhere else in the forums? Perhaps this belongs in the technical section.
Anyway, Welcome and good luck!