"Kamsahamnida" or "komapsumnida"
Kahm sah hahm nee dah
Koh mahp soom nee dah
More informally, you could say
Koh mah wuh yoh
Kamsahamnida 감사합니다 is more formal. It comes from Chinese, and also exists in Japanese (感謝 though it is rarely used there) The word is "kamsa" and has "hada/hamnida" added to the end to make it a verb. Foreigners in Korea all know this word, whether they speak Korean or not.
Komapsumnida 고마워요/고맙습니다 is less formal, and is a native Korean word. It is a verb on its own. Foreigners don't usually use this word. An astute Korean will sometimes notice this, and using it can let someone know that you actually speak the language.
If you say kamsahamnida, no one will mind, though.
A very informal, cutesy way of saying it is "kamsa-kamsa."
edit: Some of the spellings and pronunciations people have given are wrong. Most are right, though, even some of the ones that differ from mine. Korean transliteration is kind of ambiguous, and the only official systems will be impossible to pronounce correctly by someone who doesn't know them. (gomaWEOyo, for example)
1 1/2 years of full-time study, almost 2 years in Korea.