Saying and seeming
demek is to say — and, just as usefully, to mean: Bu ne demek? — What does this mean? You already meet it inside yani (that is to say).
görünmek is the passive-looking partner of görmek: not to see but to appear, to seem. Yorgun görünüyorsun — You look tired.
Wishing, carrying, catching
dilemek is to wish, the verb behind özür dilemek (to apologise) and başarılar dilerim (I wish you success).
götürmek is the counterpart of getirmek: to take something away from the speaker. English uses take for both directions; Turkish does not.
yakalamak is to catch — a ball, a bus, a thief, a cold.
Three more nouns
fark is the difference behind fark etmek (to notice). özür is the apology behind özür dilemek. And akıl is the mind — Turkish locates thought there, as in aklımda (on my mind).
can is life or soul, and it is everywhere in affectionate speech: canım is a term of endearment for a person you are fond of.