When flying from the US to Luxembourg, you may need to connect through a gateway city in the US whose airport has direct flights to Luxembourg. Such airports are listed here:
Unless you live nearby one of the gateway cities listed above, you will probably first need a domestic flight to that hub airport. From that hub you would then take a non-stop flight to Luxembourg to complete your flight from the USA to Luxembourg. An international arrival airport in Luxembourg is LUX (Luxembourg-Findel International Airport).
It is also sometimes possible to create an itinerary from a US city to Luxembourg which connects through an airport in another country, but for many travelers flying from the United States that may mean two connections and a longer flight. Hope this page helped you in planning flights to Luxembourg.