Please note that information here, whilst true to the best of our knowledge, is not legal advice and when dealing with taxes you should seek the help of a qualified tax lawyer or accountant who will make you pay for the privilege of counting how much money you should give to the government.
How much and when you pay tax will depend to a certain extent on who you are and where you are and how long you have been there.
First, however, remember that you will in all likelihood be subject to local tax which is generally deducted at source. This means that if you are working in China or South Korea you will pay tax in those countries. This is normally sorted out by your employer and is usually fairly straightforward.
Note also that:
The key to a lot of taxation - except for Americans - is one of residency. This means that if you are resident in a foreign country then you have no obligation to pay tax in your home country.
What counts as residency varies. In the UK you must be living outside the UK for at least 183 days per year to be classed as a non-resident and therefore have no tax obligation to the UK.
In Canada you need to show that your primary country of residence is not Canada - that your house or family are not in Canada and that you do not have health insurance or bank accounts there either.
Regardless of this, however, even if you do not have residency abroad, there are normally tax agreements which mean that you will pay tax only in one country and not be subjected to double-taxation on the same income.
If you are an American citizen then you are subject to US income tax regardless of where you are living. This applies whether this is your first year living abroad or whether you've been out of the US for 20 years.
First, however, is deciding if you need to file a tax return. If you earn less than about $9,000 a year then there's no need to file a return. But bear in mind that if you don't file a return and the IRS think you should have filed one, they can fine you for it; sometimes it is better to file a return just to keep the IRS happy and to show proof when you return to the US that you don't owe anything.
Of course if you receive more than $9,000 you should file a return and claim back any tax you have already paid in the country where you are living. You should also include in your return "perks" such as if your employer gives you free accommodation (where you put down a reasonable market value) or return air tickets and suchlike. (Interestingly if staying in the employer-supplied accommodation is a condition of getting the job then it does not have to be included in your tax return.)
To exclude foreign income from your tax you need to be resident abroad. By US criteria this means you should be able to show proof that the country is your usual place of residence (i.e. you live there, have accommodation there, utility bills or ties of some kind). By the way, this does not mean you have to sever ties to the US where you can still own property and visit on holiday!