The treatment to ameliorate double taxation of foreign income, really depends on your longer term plans. Let me explain :
(a) you as a US citizen/resident ( Green Card ) worked in the USA for 8 months -- Jan 1st through Aug. 30th.. 2018
(b) you then moved to country A and worked for the rest of tax year , employed by a local subsidiary of your US employer ( thus a local entity).
(c) You then move to country B and continue to work there for the rest of the following year 2019
In such a case you will not pass the Physical Presence Test till Aug 31st of 2019. Hence your best option is to ask for an extension and file your 2018 return ONLY after you pass the Physical Presence test. Your test period is September 1st. 2018 through Aug 31st. 2019 ( you start counting the 365 days from the first full day you are abroad - since you arrive on 31st. of August, that day does not count ). This means you get to exclude approx. 4 months worth of actual or allowable maximum annual limit of foreign earned income.
In another case , same as above except that on Jan 1st. 2019 you return to the USA and thus will not have a chance to meet the above exclusion scenario ( Physical Presence Test.). In such a case you file as normal your 2018 return, include your foreign income as foreign income ( not US sourced --W-2 ) and apply for foreign tax credit using form 1116. Or you can use schedule -A and deduct the foreign tax under State & local Tax, The problem with the former ( tax credit ) is that while the foreign tax credit is recognized in full but only a portion is allowable ( based on a ratio of foreign income to world income )-- the un-allowed portion of the credit can be carried forward but to use it you still must have foreign income. The issue with deduction is that the 2018 TCJA, limits the SALT to $10,000 and therefore may not be very useful.
Does this answer your query or do you need more help ? If you need more focused answer please provide more details of your situation ( e.g your longer term plan, employer abroad, how paid, connection to USA etc. )
