Assuming you had income - as US citizen - you are required to file a fax return and report your worldwide income.
Filing requirements (based on income level ) are listed in IRS publication 501 - http://www.irs.gov/pub/irs-pdf/p501.pdf
If you are living abroad - you may claim a foreign earned income exclusion.
The person may qualify for the foreign earned income exclusion - he/she should:
-- Work and reside outside the United States for at least 330 days during the year, or
-- Meet either the Bona Fide or Physical Presence tests.
If the person qualifies, he/she may exclude up to $91,400 (2009 in foreign wages -- plus housing allowances (limited to 30% of the earned income exclusion).
To receive that exclusion - the taxpayer should file either form 2555 or 2555EZ.
Here are forms you likely need:
Please be aware that - the exclusion above will not affect self-employment taxes - only income taxes. Only earned income is excludable - income from wages and self-employment. For instance - dividends, investment income, rental income, etc - are not excludable.
Please also be aware that this credit is not granted automatically - you need to file a tax return and claim the credit.
If the same income is taxable in the US and in a foreign country - you may claim a credit for taxes paid in a foreign country on your US tax return.
To determine the amount of credit -the person should use the form 1116 and attach it to the tax return. - http://www.irs.gov/pub/irs-pdf/f1116.pdf
Here are instructions - http://www.irs.gov/pub/irs-pdf/i1116.pdf
Let me know if you need any clarification or help with reporting.