Schools in Asia which offer accommodation as part of the contract often own a small apartment or two near to the school, specifically for housing teachers. This means you may be sharing with another native English speaker teacher or two which usually is of great help to you settling in. Some schools will give you the option of provided accommodation or extra cash which you can spend yourself on a place you have chosen.
Schools in some countries in the Middle East normally provide teachers with a very pleasant home environment free of charge and suitable for housing you and your family. Note that these high-paying roles are not usually open to teachers without extensive teaching experience.
If you are teaching with a governmental program, such as the JET program in Japan or the Ministry of Education program in Georgia, then you will normally be provided with accommodation (a small apartment in the case of Japan, a room with a local family in the case of Georgia and other developing countries).
If you would like to find your own place but need somewhere to stay for the first couple of weeks, the best suggestion is to speak with your employer first. They may be able to provide you with short-term affordable accommodation close to your school so that you can view different types of accommodation before making a decision. If not, do a search for backpacker or hostel accommodation in the town or city. Not only are these places cheap, they are also great places to meet other people and ask for advice on topics such as housing. They are pretty much essential if you have to have an interview in-person such as for most positions in Latin America. You could also consider the website Couchsurfing.
Another tip is to ask your employer what the previous native English speaker teacher did in terms of accommodation. Ask this question before you arrive so you have plenty of time to plan and conduct research online.
Be warned that in some countries such as Indonesia, if you wish to rent a small apartment for a year you need to pay the whole year (or sometimes 6 months) upfront. This can be very difficult indeed and you are advised to ask at your school about the possibility of the money being provided by them and paid back via monthly deductions throughout the whole year. The other option in Indonesia is the ‘kost’ or ‘kos kosan’ which is a cheap boarding house. These are affordable en-suite rooms which are paid for on a monthly basis.
Summer school positions are almost always ‘live-in’ residential courses lasting several weeks. It is rare for teachers to have to worry about finding accommodation when teaching at a summer school simply because it is normally part of the standard package you are offered.
Some employers offer an accommodation allowance above and beyond your regular salary. These include most positions around the world with the British Council (who also provide a very pleasant ‘settling-in’ allowance), plus many schools and language centres hiring TEFL teachers for Malaysia, Indonesia, Japan, Hong Kong and Turkey.