I worked three month abroad and need to report on Form 1040 foreign earned income. Where do I report the income I earned from the foreign country and where do I report the tax withhold by the freign country?

Do I need to report the foreign earned income on my state tax return as well?

It is reported on the same line where you report similar income. Then you will complete Form 1116 for foreign tax credit.

Read: Your U.S. Tax Return: U.S. Citizen or Resident with Foreign Income