There are two possible routes.
Originally Posted by holly_sparrow
 Work illegally on a tourist visa which runs from 3 to 6 months, depending on the country. I wouldn't advice this, though, as it's, ahem, illegal and so if you're caught ... well, you know... fines ($$) and worst case, deportation.
 Work legally on a working visa, which, by the way, is valid for a year, and most if not all companies expect you to stay the full year. Getting out of the contract requires a release letter from the company--in most countries. There's always the real possibility of signing a 6 month contract with the company, though, on a one year working visa. I suggest this route.
Note, you'll need a BA to get a working visa (to work legally). Most countries these days also require TEFL or CELTA--CELTA usually.
Originally Posted by holly-sparrow
Japan: good money, but competition abounds, and the stay can feel isolating at times, even in the biggest cities.
[I lived there for 6 years]
Italy & Spain: Have friends who teach there, but last time I checked, you need a EU passport to work in Europe. This could have changed, though. Moreover, they tend to prefer teachers from the UK and the USA.
Morocco: Political ... Have friends who visit twice a year on vacation and had looked for teaching jobs. They suggest against it.
Brazil & Chile: Safety ... Have friends who taught in both places and they suggest against it, at least for right now.
Vietnam: Go for it.
Singapore: Go for it.
China: Go for it.
South Korea: Go for it.
Russia: Go for it. <surfing though?>