How do you report foreign income earned by a resident alien (qualifies as a resident alien for the full calendar year as per Green card test) if the alien does not qualify for the exclusion? By how, I mean where on the 1040, which form do you use? Do you have to complete form 2555 if you do not qualify for the exclusion? Or do you report any foreign salary and self employment income under other income and any foreign tax paid on form 1116?

“How do you report foreign income earned by a resident alien (qualifies as a resident alien for the full calendar year as per Green card test) if the alien does not qualify for the exclusion?”-->Then you can claim your foreign tax credit on your US returns, both federal and state returns, on your income taxes that you paid to a foreign taxing authority(ies) on your earned income in the foreign country by filing Form 1116. You can claim a credit only for foreign taxes that are imposed on you by a foreign country; Foreign tax credits allow US taxpayers, I mean US citizens or US residents UNDER either US INS Rules or UN Tax Law, to avoid or reduce double taxation. You can claim FTC on 1040 line 47 or you can itemize foreign tax on 1040 Sch A line 8, I guess. To claim FTC, you meet the requiremnts; the tax must be imposed on you; you must have paid or accrued the tax;the tax must be the legal and actual foreign tax liability;the tax must be an income tax (or a tax in lieu of an income tax).
“ By how, I mean where on the 1040, which form do you use?”- You need to report FTC on 1040 line 47 or on Sch A line 8. The foreign tax credit is intended to relieve you of the double tax burden when your foreign source income is taxed by both the United States and the foreign country. Generally, if the foreign tax rate is higher than the U.S. rate, there will be no U.S. tax on the foreign income. If the foreign tax rate is lower than the U.S. rate, U.S. tax on the foreign income will be limited to the difference between the rates. The foreign tax credit can only reduce U.S. taxes on foreign source income; it cannot reduce U.S. taxes on U.S. source income. An itemized deduction only reduces your taxable income, whereas an income tax credit can provide a dollar-for-dollar reduction of your actual tax liability. For example, if you're in the 30% income tax bracket, a $200 deduction would only reduce your taxes by $60 (assuming full deductibility), whereas a tax credit would provide a $200 reduction in tax liability (if you are eligible for the entire credit). The amount of foreign tax credit you're allowed to claim is limited to the lesser of the amount of foreign tax paid or the US tax liability on the same income. For example, let's say you receive $1,000 in foreign dividend income and pay $350 in foreign tax, but only owe $250 in US tax on the same amount. In that case, your credit is limited to $250. If your US tax liability were the same or higher than the foreign tax paid, you would be eligible to claim the full credit. In other words, you avoid double-taxation but always end up paying tax at the highest tax rate. If you paid more foreign tax during the current year than you can claim as a credit, you can carry back the excess for one year (that is, file an amended return for the previous tax year) or forward the excess for 10 more years. The ability to carry back or carry forward any unused tax credit only applies if you file Form 1116, and is restricted by the amount of excess limit available in those carryback or carryforward years.
“ Do you have to complete form 2555 if you do not qualify for the exclusion? “----> No; as said above, you need to file Form 1116 to claim your FTC.You need to file Form 2555 If you qualify FEIE.
“Or do you report any foreign salary and self employment income under other income and any foreign tax paid on form 1116?”---> Correct; on Form 1116.

Thank you, Wnhough.
My question was more "Where do you report the foreign income?", than how do you claim the credit? So QUESTION: Where do you report the compensation (salary) received in a foreign country? What about self employment income received in that foreign country? (The compensation amount listed on form 1116 is used only to calculated the general income limitation) and it doesn't carry to page 1 of 1040. So do you report it as other income, considering it can't be reported as W-2 income?

Thank you

“My question was more "Where do you report the foreign income?", than how do you claim the credit? So QUESTION: Where do you report the compensation (salary) received in a foreign country?”---->On form 1116 Part 1 line 1a as General Category Income; general category income may include: Wages, salary, and overseas allowances of an individual as an employee;Income earned in the active conduct of a trade or business;Gains from the sale of inventory or depreciable property used in a trade or business.
“What about self employment income received in that foreign country? (The compensation amount listed on form 1116 is used only to calculated the general income limitation) and it doesn't carry to page 1 of 1040.”---->You need to include income in the category checked Part I , b that is taxable by the United States and is from sources within the country entered on line g. You must include income even if it is not taxable by that foreign country. You need to check b. SE income is general category income that is income that is not passive category income but it is income earned in the active conduct of a trade or business. You need to report your taxable income or (loss) from sources outside the United States on Fomr 1116 line 14 and 16(net foreign source taxable income) and need to enter the amount from Form 1040, line 41.
“ So do you report it as other income, considering it can't be reported as W-2 income.”---> As said above, report it on Form 1040 line 41.