In South Korean culture you will find South Koreans are reserved and well-mannered people. South Korea is a land of strict Confucian hierarchy and etiquette. As a visitor, you will not be expected to know every nuance, but making an effort will certainly be appreciated.
Following these rules will impress the locals:
Koreans bow to each other to show their respect when they meet. They may also shake hands. However, with people you know well, a quick nod of the head and a simple annyeong haseyo meaning "hello," should suffice the direct translation is "do you have peace".
When meeting for the first time, older Koreans will tend to ask about your age, your parents' jobs, your job, and your education level. If you feel uncomfortable about the questions, just provide short answers and discreetly try to change the topic if possible.
When picking something up or taking something from somebody older, always use two hands. If you have to use one hand, you can simply support your right arm with your left hand. Likewise, when shaking hands with somebody older support your right arm with your left hand.
It is customary to take off your shoes in houses and in many traditional restaurants.
Koreans, in general, have very strong nationalistic views and would view any criticism of their country with varying degrees of hostility. To avoid getting into the bad books of your hosts, it is advisable to praise the country or, at least, to avoid bringing up anything negative about it.
Avoid bringing up the Japanese occupation, Dokdo, the Korean war of the early 1950s and US foreign policy, or engage in other political discussions (unless mentioned to you) as these delicate topics are likely to get you on someone's bad side and can lead to intense debates, use of negative epithets, or even violence. Also, do not attempt to compliment North Korea in any way.
South Korean households may have strict rules about recycling, for example, one bin may be for paper only, as to another in the kitchen for food/drink containers.
Do not pour your own drink, but do pour for others. When dining with Koreans, the oldest always eats first. It is common to hear people talking loudly in restaurants, as a sign of being happy and enjoying the food. Also, slurping noodles is actually expected, as it shows that you enjoy the food and you are appreciating the cooking well.
Like other Asian countries, when giving tips in restaurants, it is polite to fold the bill and hand it into the waiter's hands secretly and quietly, rather than leaving it on the table or displaying/waving the bill in full shape like the social norm in Western countries.
Similarly, in households, when giving money to younger people, it is more acceptable to fold the money and place it in a piece of paper, preferably an envelope.
The further you are away from metropolitan areas the more conservative the people are.
In South Korean culture swastikas are commonly seen in Buddhist temples. They are a religious symbol and do not represent Nazism or anti-Semitism, so visitors should not feel offended when encountering them.