The first piece of advice, however, is to do all the necessary research about the employer, the country and the city in which you will be living. The more research you have done in advance, the less chance there is of you being shocked and wanting to leave simply because you don’t like it for some reason and would prefer to be back in your home country. It can take time to settle in to a new way of life.
Note that if you don’t have a contract or a Work Visa sponsored by your employer, then you are not really bound by anything other than good manners to continuing working there. It does look much better on your CV if you have stayed with the same company for at least a year, but there are often things which are more important to consider.
There are some very legitimate reasons for wanting to finish early that no amount of research could prepare you for. If civil war breaks out in the country you are teaching in, or some other sort of political unrest suggests that foreigners would be better off leaving, then you are well within your rights to leave without completing your contract term. All good language centres and schools include of clause which deals with situations of this sort, so be sure to check for it before signing.
If a family emergency happens back in your home country and you need to dash off at short notice, you should be able to come to an agreement that suits both you and your employer, and anything of this nature is usually looked upon sympathetically.
A common reason for wanting to leave early is because you have made lots of local contacts over the previous few months and have been offered a job at another school with a higher salary, more annual leave, and better conditions generally. This happens all the time and is made trickier if the school offering you better conditions only hires at one particular time of year!
In these circumstances, you will have to negotiate with your employer in order to find a solution which satisfies both parties. The main issue for your employer will probably be to do with any fees paid for you to work legally in the country and relevant paperwork for national authorities such as immigration.
The reason that language centre owners like you to teach for at least one year is that the money spent on the visas and airfares and so on can be recovered over the course of a year. If you want to leave after just a few months, they may have made a financial loss overall. Therefore, you might be asked to pay some kind of fee to make up for whatever they have lost pro rata, or to not receive your return airfare. This is usually pretty reasonable, but it depends on the particular circumstances and length of time you have been an employee there.
Note that once you have terminated your contract with your employer, your right to stay in that country will end shortly, especially if you are on the standard Work Visa. You may be given a few days to leave the country by the immigration authorities, after which you will return once again if you are taking a second job in the same country. It can be difficult to get the timing right between ending your previous contract and starting you new one, so discuss this in detail with your future employer if this situation applies to you.
Some countries, including Qatar and Indonesia, will not allow you out of the country without an Exit Permit. These dubious stamps in your passport effectively keep you in that particular country unless your employer (usually your work visa sponsor) agrees to you going abroad even if it is just a short holiday in a neighbouring country.
Most employers are fine with you holidaying overseas, especially as you will probably be the one paying for the Exit/Re-entry Permit rather than them, but it can obviously cause serious problems if you have an argument with your employer. Without their permission, how can you properly terminate you contract? This situation is weighted in their favour so it is essential to reach an amicable agreement.
If you cannot see eye-to-eye with your employer and just want to get out of there as soon as possible you really have two main options. The first is to seek legal advice, which can be difficult and costly for an expatriate. The second is to continue working for them, and ask for an Exit-Re-entry Permit for a long weekend in a neighbouring country. That way they will assume you are returning, as you pack your suitcase and leave the country for good!
Hopefully the above scenario will never happen to you but from time to time it does. If you genuinely aren’t happy and can’t see a way to continue in that particular country then moving on to another country may be the best idea.