Deciding to go to a foreign country and teach English is a big decision and should not be undertaken lightly. There are many things to consider before you take the plunge. One thing you need to decide is where in the world you are going to go - there are many places where English is still in hot demand and you will be able to find work. Each place has its pros and cons so my advise is to do your homework - decide what you want and then find the place that best meets all of your needs.
For me South Korea was the most attractive because of the benefits it offers, while some countries offer a higher pay rate like Japan and the Middle East, most jobs in South Korea will offer airfares to and from your country, paid housing and a bonus on completion of your contract. I was also interested in exploring a country that to most people is unknown. If you ask someone what they know about Korea the usual answer is - the Korean War, the separation of the North and South and that they had the Olympics there a while ago. There is of course a lot more to Korea, it is a place of rich history and interesting culture.
There are also many volunteer opportunities for teaching English which you may like to explore, this is where you get paid a very small amount to live on and you may be provided some accommodation living with a family in country. Its a great way to give back and you could have some really unique experiences.
You will also need to take into consideration the requirements for teaching in the country that you wish to go to. Most jobs will have as a minimum that you have attended an English speaking high school and that you have at least a Bachelor's degree from an English speaking university. While there are some people who have managed to get a job without a degree, it does make it much harder and it may not be a very reliable position. Another thing is whether or not to do a TESOL course. Many jobs do not require it and lots of people will say not to bother, however if you do have one it can open up other opportunities that may not be available to people who only have a degree.
I myself did a TESOL course about a year before I came over to South Korea and I am very thankful that I did. I had no idea what I was getting myself in for and no real concept of what teaching was like, doing the course really helped me to understand what I would be doing and gave me a chance to get prepared for my time in the classroom. I looked at a lot of the courses available both online and in my country and decided that I wanted one that had at least a small part of the course taught in the classroom. That limited my options to courses run from New Zealand and I narrowed it down to two options - they both had information sessions which I attended where they tell you all about the course, what they will be covering and what you can expect to walk away with. In the end it came down to the fact that one offered a practical teaching component as part of the requirements and it also helped that the presenter was really passionate about her experiences and really good at conveying that passion.
The course I chose was run by an Australian company called Teach International ( http://www.teachinternational.com/) and it has a number of location and course options. The certificate that I did included a one week in class component scheduled around a full time working week, after 5pm and on the weekend. I was still employed at the time and would not have been able to get the time off so this worked out really well for me. There was also an online component where you had to complete a compulsory unit of grammar (a great reminder and I even learned some new things) and two elective units. The other part to the course was the practical teaching component, this was a bit harder as the company had not set up any work experience places in Wellington where I did my course. I ended up sorting out my own placement just by contacting a local English Language School, they were only too happy to help out and I really learned a lot. It was great to have that chance to get up in front of a real class and see what it was like.
I would very much recommend Teach International if you are thinking about doing a TESOL course from New Zealand or Australia. They also have some options where you can do the course in a foreign country like China or Turkey which sounds really exciting. It is a lot of money to put up but I think that it was well worth it and it can open doors when it comes to finding a really great teaching job.
Once you have decided on the country that you are going to go to you can start looking for jobs and do some research on the country. You will need to know the visa requirements for living and working there. Its a good idea to make sure you know some background information about the country that you choose as it may come up in an interview for a job. They might ask you what you know about the country or why you want to visit. If you have done your research you can let them know that you have been actively learning about their country and have your answer all prepared so that they feel like you are really interested and eager to get involved.