When flying from the US to Fukuoka, you may need to connect through a gateway city in the US whose airport has direct flights to Fukuoka. 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 Fukuoka to complete your flight from the USA to Japan. An international arrival airport in Fukuoka is FUK (Fukuoka Airport).
It is also sometimes possible to create an itinerary from a US city to Fukuoka 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 Fukuoka.