As mentioned previously, you'll find living and working in Korea leaves you with a fairly high disposable income. So you won't have trouble making ends meet once you start getting paid, but that first paycheck is a month away after you start working. So how much should you bring to tide yourself over until then?
Well, most veterans who are here to save money and are savvy with bargains, will tell you that they can live off of 10,000won/day. That's about 300,000won/mnth. That's really tough to maintain, especially if you plan on having a social life. To pull this off, one would need to have a rice cooker and be eating Korean food at home, likely purchased in bulk to take advantage of the savings. Also owning a bike to commute to school or elsewhere would help avoid subway and transportation costs, which can creep up to 2-4000won a day, depending on how busy you are. And eating at pojangmachas or cheap places like Kimbap Cheonguk or Hansot Dosirak. Or sleeping at jjimjilbangs when traveling in different cities, rather than staying at motels. Living off of 300,000won/mnth can be done. But it requires discipline and some local knowledge of your surroundings.
On the other end of the spectrum, if you like to eat at Bennigans and Outback a lot, party at the bars, travel outside of Korea on long weekends and holidays, you can do all of that, as well. But your whole budget will be shot.
Realistically, expect to go through 20-30,000won/day until you get yourself situated. You likely won't know of cheap bargains or cheap places to eat right from the outset and will likely find yourself slipping into no-hassle food environments like KFC and Burger King, maybe a little more often than you may expect. Once you get familiar with Korean menus, where to shop and eat for deals, then you can expect your daily expenditure to drop. Possibly lower than 20,000won. But some days, you'll blow 50,000won on stuff and then 2000won on the next day. It really depends. But bar none, how much you drink and where you eat, will usually hit the wallet the most.
So, if you're coming over already with a job lined up, it'd be helpful to have about $700-1000 for the first month. If you're coming over for a job hunt and plan on signing a contract in Korea, then you might want to bring at least twice that, just in case. If you're not terribly picky, you can line up a job within a week or so, but if you have particular preferences, then you might need to hunker down for awhile and should be ready for that.
As a last resort, many employers will not usually let their employees hang out to dry in a financial situation. Although it is humbling and may reflect a little embarrassment on your part, you can ask for a pay advance if it came down to it. Not all schools oblige to this, but most seem to accommodate somewhat. You shouldn't factor this into your budget, as not only does it place a bad first impression on you, but also, it can be tough to get your head above water, if you are chronically asking for advances.
[edit] How should I bring money?
Well, obviously, having a credit card to fall back on would be ideal. Barring that, it'd be wise to take a good chunk in cash and the rest in traveller's checks. Bringing an international bank card is ok, as Korea has loads of ATMs, but you'll find that some are finicky and might not always accept your card. So rather than trekking in between ATMs to see which one likes your card, bringing traveller's checks tends to be a more reliable option. Any bank will cash these and you really don't need to know much Korean to explain what you want done, once you slap down the traveller's check and your passport in front of the clerk.
As for where to exchange your money into Won, some people like to nickle and dime over exchange rates and refuse to do so at the airport. But if you don't want to exchange all at the airport, then at least exchange some. As in ensuring that you have at least 100-200,000won, until you can get situated and figure out where a bank is to exchange the rest. Walking out of the airport without exchanging some of your money into won in hopes to exchange at a bank later, is a really bad move, yet some teachers make this mistake. If you are at the baggage claim at Incheon Airport, the currency exchange will be right past customs, but before you go through the exit doors to the main concourse.
[edit] See Also
