Culture
Best ways to quickly embarrass yourself.
I've been to China a couple times and to Japan very briefly, in addition to living in Korea for a year, and from my limited knowledge Korea and America are the most similar. There are still differences--at times large--and this page will provide a brief glance at some of those differences. Luckily, however, Koreans are very forgiving of foreigners who commit social faux pas, so don't worry overmuch.
In Korea, much of what is polite or rude is dependent on your place in society and the place of the person you're interacting with. That's true in almost all societies, but even more so in Korea. Age and job seem to be two of the most important factors, so if someone's just 1 year older than you they may treat you differently than if they were just 1 year younger. However, if you're a CEO of a company and the other person is a janitor of a completely different company, that's going to factor in more than age, to a certain extent. It's a difficult sea to swim, but if you're polite to anyone who's not significantly younger than you, and not rude to anyone, you'll do fine. Oh, and almost none of this applies if you're good friends with the person.
Culture
You will need to use your right hand in all things when interacting with others. This mostly occurs when giving or receiving something. To be more polite, to your boss or those who are higher than you in social standing, use both hands to give or receive instead. When pouring alcohol, use both hands, and when someone's pouring alcohol into your glass, hold the cup with two hands. Pouring any other liquids doesn't matter, but to be safe I always use my right hand.
When eating out at a Korean restaurant, you aren't supposed to tip. Lots of foreigner-run establishments assume you'll tip the bartender, or may have a tipping jar at the register, and some cafes are beginning to get those jars, too, but otherwise, don't tip. Yay!
Blowing your nose at the dinner table is the equivalent of farting loudly while eating; don't do it, ever. It's ok to blow your nose at other times, but don't do it loudly. Wiping your nose is perfectly ok, and absolutely necessary as most Korean food is spicy.
Like Japan, you don't wear your shoes inside a person's home or a restaurant, as well as miscellaneous other places. Most buildings where you're required to remove your shoes will have a small foyer and cubbyholes for shoes.
Spitting on the sidewalk is incredibly common, and not just saliva but mucous. This is probably a result of looking down on blowing your nose. Anyway, it can gross people out, a lot.
As a people, Koreans are usually quiet and reserved. There are of course lots of exceptions, especially while people are drinking, but it's not uncommon to see old friends run into one another on the street, and exchange only a glance, or a polite hello, for example. There's nothing wrong with that, but as most foreigners are louder and more boisterous, some Koreans will be upset with you if you disturb their peace. The subway is about as quiet as a library, which will be a complete shock to some, and you should not speak loudly there, for instance.
Housing
The housing most schools and hagwons provide is small, usually with a bathroom, kitchen, and main room. Sometimes the main room and kitchen will have no partition between the two, so there are only 2 "rooms." My first apartment had a kitchen, bathroom, and main room, all separated by doors. My second room had a bathroom, main room, and bedroom, all separated by doors. Other apartments usually have one of those two configurations, or just a bathroom and main room.
My favorite thing about Korean housing is that the hot water pipes run through the floors, which is the way your entire apartment gets warm: from the ground up. It's amazing to get out of bed on a cold winter morning and put your foot on a warm, hardwood floor. It's efficient, as well.
I can almost guarantee your that your provided apartment will not have a clothes dryer or dishwasher. Both of these are available, but not typically in a studio apartment. To dry clothes, almost everyone uses a clothes drying rack, such as this one. To wash dishes, almost everyone uses hands, like these. Most apartments and homes also lack an oven of any kind. The only one I ever saw looked just like a microwave, and was separate from a stove. They do have range tops to cook on, however.
Korean bathrooms look something like this. There are no shower curtains so water gets everywhere, but that's by design. The toilet lids prevent water from getting on the seat, fortunately, but everything else will get wet. This makes it very easy to clean, as I just sprayed a 1/10 bleach/water solution everywhere, daily, then rinsed it off while showering. Koreans use shower sandals to keep their feet from getting wet or dirty.