The very first thing you really must do when you are trying to learn Korean, even if its only enough to get you through a short vacation in Korea, is to learn Hangeul (한글): the Korean alphabet. It will only take a few hours of your time to memorize which sound corresponds with which character and how to combine those sounds together, but it is oh, so worth it, and will make your time in Korea exponentially easier.
There are 24 different Hangeul letters of which 14 are consonants and 10 are vowels. It was developed as a writing system by the great King Sejong in 1446, and was specifically designed so that even commoners could learn to read and write it.
It has been called 'the language you can learn in a morning' and is associated with this very popular Korean quote, "A wise man can acquaint himself with them before the morning is over; a stupid man can learn them in the space of ten days." It is of course easier to learn when you actually have a background in speaking Korean to associate the sounds with, but you can still do it! Try it out!Here is a list of Korean letters matched up with their closest English equivalents. I know that there are more than 24 letters listed here, but if you look closely you'll see that the extra ones are only common combinations of the simple letters. Good luck!