Right Alt key used as Hangul(Korean)/English toggle, right Ctrl key as Hanja.
When toggled to Hangul, only English characters are overridden by Hangul characters. All numbers, symbols are also same when you are in English typing mode.
Basically no additional key in there compared to QWERTY.
Is that complex and hard learning type in Hangul? Nope. Maybe 'Korean' is complex to learn, but 'Hangul' - I mean, script? character composition system? sort of that - is quite simple.[2]
Actually It's capable of implement more efficient input layout than English especially more restricted environment. Like basic cell phone key layout(E.161).[1]
There was a King, and He was really great hacker. Because he was a King, he grabbed bunch of smart guy all around country. ; ) Then push them working hard. (did I said he was King?) Therefore, invented many good one for country people. Today Korean has own quite good and expressive characters and he deserved quite good place.[3]
[0] http://i.imgur.com/j0Xk6oY.jpg
[2] http://blog.naver.com/PostView.nhn?blogId=neraijel&logNo=110...
Other countries that make even less sense and use way too many special characters (from my blunt perspective) usually have different keyboards. Prime example that I know of is France where you have to use the shift key to make numbers.
To answer what you actually asked: Yes we are taught how to make those special characters. For me it's as logic as typing parenthesis or the euro sign, but I'm spending most of my waking hours typing one thing or another. Many people don't or barely know how to.
It's not what most of the time is spent on in those courses. We're being taught the asdfjkl; row just like everyone else. Or aoeuhtns, depending on your keyboard (in the Netherlands we only have qwerty though). Making accents is more of a side thing that's mentioned once or twice after learning everything else at an acceptable speed.
* We should|could|would|must|might|ought to|need to get rid of other overhead.
* You should|could|would|must|ought to|might get rid of other overhead.
* Those guys over there should|etc. get rid of other overhead.
* I can't type "ride". What does "...ride other overhead" mean? I dunno, but people write incoherent things all the time.
IOW, what you think of as "overhead" probably isn't, especially with natural language.
Chinese input methods typically require a sequence of key-presses and then a selection from a menu of matching characters, with the most common matches first. Multi-character sequences can be entered without making a choice until the end, in which case the most likely n-grams come first.
Most people in Taiwan learn phonetic (Zhuyin) in school, which is very easy, as long as you know standard pronunciation.