Honorifics
When talking about someone superior in status, a speaker or writer to use special nouns or verb endings to indicate the subject's superiority. Generally, someone is superior in status if he/she is an older distant relative (grandparent's sibling, older sibling's spouse, etc.), a stranger of roughly equal or greater age, or an employer, teacher, customer, or the like. Someone is equal or inferior in status if he/she is a close relative (grandparent, parent, spouse, or sibling), younger stranger, student, employee or the like. On rare occasions (like when someone wants to pick a fight), a speaker might speak to a superior or stranger in a way normally only used for, say, animals, but no one would do this without seriously considering the consequences to their physical safety first!
One way of using honorifics is to use special nouns in place of regular nouns with "honorific" ones. A common example is using jinji instead of bap for "food". More often, special nouns are used when speaking about relatives. Thus, the speaker/writer may address his own grandmother as halmeoni but refer to someone else's grandmother as halmeonim. (The m comes from the honorific suffix -nim (님), which is affixed to many kinship terms to make them honorific; thus, hyeongnim is the formal term for an older sibling of the same sex (derived from hyeong, the informal term for man's older brother; eonni is the informal term for a woman's older sister).
All verbs can be converted into an honorific form by adding the infix -si- (시, pronounced shi) after the stem and before the verb ending. Thus, gada ("go") becomes gasida. A few verbs have special honorific equivalents. Therefore gyesida is the honorific form of itda ("exist"); japsusida is the honorific form of meokda ("eat"); and jumusida is the honorific form of jada ("sleep").
A few verbs have special humble forms, used when the speaker is referring to him/herself in polite situations. These include deurida and ollida for juda ("give"). Deurida is substituted for juda when the latter is used as an auxiliary verb, while ollida--which literally means "raise up"--is used for juda in the sense of "offer".
Pronouns in Korean have their own set of polite equivalents: thus, jeo is the humble form of na ("I"); jeoheui is the humble form of uri ("we"); and dangsin ("friend," but only used as a form of address and more polite than "chingu", the usual word for "friend") is the honorific form of neo ("you" (singular)).
Speech Levels
There are no fewer than 7 verb paradigms or speech levels in Korean, and each level has its own unique set of verb endings which are used to indicate the level of formality of a situation. Unlike honorifics--which are used to show respect towards a subject--speech levels are used to show respect towards a speaker's or writer's audience. The names of the 7 levels are derived from the non-honorific imperative form of the verb hada ("do") in each level, plus the suffix che, which means "body."
The highest 5 levels use final verb endings, while the lowest 2 levels (haeyoche) and (haeche) use non-final endings and are called banmal ("half-words") in Korean. (The haeyoche in turn is formed by simply adding the non-final ending yo (요) to the haeche form of the verb.)
Taken together, honorifics and speech levels form a cartesian product of 14 basic verb stems. Here is a table giving the 7 levels, the present indicative form of the verb hada (하다; "do" in English) in each level in both its honorific and non-honorific forms, and the situations in which each level is used.