Because I'm heading off to Ecuador, lots of people ask me about the visa situation so I'm doing this post to answer what I can. Firstly - I haven't even tried yet and am going in a slightly dodgy way. I am not an expert and everything I write here I have gleaned from internet research. I would insist that people ask someone who's gone through it all, but internet isn't so widely available there so I'll say what I can and try to update it as I find out more. Any contributions welcome, especially from anyone who knows more that me! (Kallen??)
I'm going on a tourist visa and then the school will take me to Peru to get work visa. This is because by all accounts it's much harder to get one from the UK as they over-analyse. Lots of people think it's dodgy to go this way and that this will somehow put me in the hold of my employer.. I say this is a state of mind. South America is a sketchy place and you have to accept that if you want to go there. You can't have freedom and security at the same time in my book!
To get a work visa as far as I know you need a degree and/or your TEFL cert, and a CRB check - not the enhanced one you get here - more on this in a minute. You need to get your certificate apostillized (google 'apostille services UK') You then have to go to a third country with the contract of employment from your school, it costs currently $230 US.
Go to the website of your local police force and type 'subject access' into the search bar. You are allowed by law to know what is held about you on the police national computer. You download a pdf file and fill it in. You send some ID and £10. On the form it says 'do not use this form if you are applying for a visa for the US, Canada, Australia but I think Ecuador is OK.
This is a link from a forum that is sometimes a bit negative but there is a great post from a bloke called Swimweh dated March 12th which is mostly about where I'm going but gives visa advice from someone who has been there.
Bear in mind that the lady I spoke to at the school has been there 18 months and the visa laws have changed 3 times since then. Don't expect 100% guarantees about anything in South America, although Ecuador is probably the most stable and safest country, they do have revolutions quite often. If they have one when you are there don't worry it's not usually really heavy or violent and not much changes afterwards, in my experience.
I'd advise getting a job offer and then talking to the school about their approach. If you have a degree it might be worth trying from here, I can't tell you I'm afraid. If you are in the Americas already, I'd just go and look for work. Remember, when you have your work visa you can go and look for other jobs. Sometimes you just have to take such a big risk that you thereby commit yourself to success. Good luck.