If you are a native English speaker, or speak English to a high level, then you will be able to walk into a number of different English-teaching roles in Thailand. Most folks, however, head out to Thailand with the intention of teaching in a Thai school. There are several different types of school and although you'll probably be able to find work in all of them, some will be more difficult than others.
Working as TEFL teacher in an international school in Thailand
International schools in Thailand follow an international curriculum. This might be the British curriculum, American curriculum, Australian curriculum or one drawn up by an organization like Cambridge International Examinations.
International school teach their children primarily in English although you might find French or German international schools that will use their respective languages in class. The children that attend these schools tend to be from a wide and varied background but for the most part will not be fully-Thai children. The staff will be split about 50% Thai and 50% foreign, wages will be quite high and working hours will be similar to what a school in your home country would employ.
These schools are quite rare outside of Bangkok but there are quite a lot in Chiang Mai and a few others dotted around the country, primarily in areas like Phuket and Koh Samui where there are larger numbers of expats.
TESOL teaching in a private Thai school
Private Thai schools will teach their children in Thai for the most part but it is also possible that you could end up in a bilingual school, where children receive tuition in both English and Thai. These schools are well-funded, generally quite well-run and well-equipped. They will be pretty formal (sometimes even more so than many international schools) but wages will be pretty good.
Children will be mostly Thai as will members of staff. These schools are more common than international schools but will be mostly found in major cities like Bangkok and Chiang Mai.
Working in a Thai government school
Thai government schools are found in every Thai town and city, right across the country. They are often well-equipped and funded but usually quite poor, especially when compared to a Western school. I taught in a government school for 6 months and had no air conditioning in any of my classes. Some did not even have a fan!
The children in these schools are almost exclusively Thai and the staff will be largely Thai as well. Working in this kind of school will not pay as well as a private or international school but will be a great insight into Thai culture.
Volunteering to teach English in a Thai temple (wat) school
Thai temple schools also need TEFL teachers but have no money to pay them so they do not actively recruit. If you are looking for a way to give back then just approach one of these schools (most times will have a school attached to them). This is where the children come to learn if the family have no money to pay for their education. Do not expect any payment but do expect lovely children and really friendly people to work with.