Any US Citizen or Resident Alien must file the 1040 and report their income, regardless of where in the world they are living when they make it. Or, for that matter, where in the world the company is that provides the foreign-source income.
Generally, the taxpayer is allowed a deduction for up to $87,600 of foreign-source income per person ($175,200 if both spouses qualify). There are special rules for clergy and a variety of requirements. They will file Form 2555 in their 1040 and report the foreign-source income deduction on Line 21 of the 1040.
Generally, they are allowed a credit for any foreign taxes paid. This will be reported on a From 1116, filed with their 1040, and the credit will be taken on Line 47 of the 2008 1040 tax return. While the credit is usually the preferred choice, the taxpayer may elect to take a deduction for the foreign taxes paid on their Schedule A instead.
{Notice the word “generally”? I — and the IRS — use that word when we are alerting you that there are special rules and some exceptions. If you are not finding what you expect on the tax return, see if they fall under some of the specific rules.}
IRS Publication 54 has more information. Go right to page 43 index and it hyperlinks back into the publication for the info you need.