Teaching abroad is a great way to spend time in another country while gaining work experience and earning pretty decent money to boot. There are lots of great teaching options all over the world. I have friends who have taught in Peru, Germany, Indonesia, and Japan. There are ups and downs to all locations and different motivations to chose each one. I'll be dedicating this post to teaching in Korea and will probably do a follow up about teaching in China.
There are a few things you should know about teaching in Korea-
Korea is a slightly different market than other opportunities to teach abroad. The qualifications are minimal but generally non-negotiable. The pay is pretty solid but there is often very little upward mobility. Teaching in Korea is safe, convenient and easy, but you are very much limited to teaching. If you are looking to transition into something other than teaching Korea might not be for you. But lets circle back to the pay-check again- it is totally reasonable to save $10k a year teaching in Korea. And honestly, it isn't hard to get hired having never spoken to a child before.
A job in Korea should always include these things: a flight to Korea and back home at the end of your contract, an apartment, health insurance, and a monthly pay-check of about 2 million won. Pay may vary with qualifications. If you are offered a contract that does not include these benefits you should decline. You should carefully consider your contract before signing it. It will determine how much you work, how much you get paid, your living conditions, and what benefits you get. Your contract can be enforced to the letter and any promise not written into the contact is not guaranteed.
Korea has tighter restrictions on visas than some other countries. To obtain a work visa you must a have BA degree. Unlike China this cannot be faked or by-passed because you need a copy that is certified by the government that issued the degree. You must also hold a passport from an English speaking country: those being Canada, US, UK, Australia, NZ, Ireland and S. Africa. Being a native speaker but holding a different passport won't cut it. To do anything in Korea you need an Alien Registration Card, which can only be obtained with a visa, so trying to teaching in Korea without a visa is not a viable option. The only other solid requirements are that you need to be able to pass a background check and a health check. If you have a BA, a passport from a native English-speaking country, a clean back ground check and don't have AIDS you are a shoe-in. If you don't meet these qualifications check out China.
If you meet these qualifications then the first thing to do is to find a recruiter and decide which sector you want to teach in and what kind of location you are interested in.
About recruiters- schools pay recruiters to find teachers for them so you should never pay a dime for the "opportunity to teach abroad" as they might phrase it. On that same note, always remember that the recruiter doesn't get paid unless you sign a contract so they are more interested in getting you to agree to take the job than they are in making sure you are placed in a good school. Some recruiters promise to find you another school if the school you sign with doesn't work out. Go ahead and apply with a number of recruiters and see who offers you the best options. The recruiter should also be in charge of helping you do all of your paper-work for the visa and arranging your flight. The paperwork is tedious and can take a long time so factor that into your timeline.
There are generally three teaching options in Korea: public schools, private language schools
(Hagwons), and universities. All have advantages and disadvantages.
University jobs can be hard to get, unless you are will to work outside of a major city. Most of the people that I know who held university positions got their job in Korea after having taught for a few years. These are generally the only jobs geared toward teaching adults (though there are some exceptions).
Public school jobs offer more vacations days than hagwons, but might pay less. They tend to be less risky than a hagwon job but you are also likely to be the only Western teacher in your school and you might have huge classes. The jobs are also increasingly unavailable as Korean teachers replace foreigners to cut costs. Public school jobs require a TEFL or a Master's degree. Most people that I know who have chosen this route have been very happy but I think it is an advantage to have already established a friend-base in Korea before working at a public school.
Hagwons are the most popular options but also come with a number of risks. Hagwons are for-profit language schools teaching kids anywhere from pre-K to high school. The image of the hagwon relies on having native English-speaking teachers and they are often willing to pay a premium to fulfill this. It is also important to remember that these are businesses and thus can be prone to taking advantage of teachers or even suddenly closing down without notice. It is important to research your school before accepting an offer!
Beyond considering what kind of school you want to teach in you should also consider where you want to teach. If you are applying from outside of Korea you likely have little choice or knowledge about what locations are open to you but you should consider what conditions you are looking for.
The two major cities in Korea are Busan and Seoul. There are large numbers of jobs in these cities but there are also large numbers of people looking to be placed there. Jobs in big cities often can pay less because they have more interested teachers and you should keep in mind that the cost of living is higher. Your housing will be more limited but your selection of western goods and English-speaking services will be greater.
Medium-sized cities often have a tight-knit group of expats that can be less isolating than a large, anonymous city. Unfortunately, if you don't get along with those expats you might be more isolated than ever.
Rural areas don't often see westerners and as such have added difficulties. You will be stared at, have your picture taken, and pointed at. But you will have plenty of opportunities to learn Korean and be immersed into Korean culture if that interests you.
When considering teaching abroad it is important to do tons of research to understand what you are getting into. You should also consider that what you hear on the internet (say, from Dave's ESL cafe) is going to be disproportionately negative. The majority of people who are in Korea and are enjoying their time there are not stopping to write about it on the internet. It is the people who are miserable who sit at home and complain on forums. I've only known a few people who were unable to complete their year-long contract but do be honest with yourself about your ability to undertake the huge change that is living abroad. You will at times be lonely, homesick, and aggravated with your students/coworkers/boss. Teaching in Korea can also be deeply rewarding and lucrative. It really is what you make of it.