The Americans arrived in Europe and Asia by February, 1942. They encountered a dire situation. All of Europe was controlled, in some way, by a Fascist government except for Great Britain. The German Empire stretched from France to Russia and south to the Italian Alps. In Asia, Japan controlled Korea, most of China, southeast Asia, and the islands in-between (Midway, Philippines, Indonesia, etc...). It was clear the US could not attack the empires directly. Therefore, they decided to "contract" the empires.
The US drafted more than 18 million soldiers for World War II - the largest American military in history.
The "Game Plan"
"Germany First" = the United States interests lay mostly in Europe. It is where our alliances were found and where most of our trading partners reside. The US decided to focus on defeating Germany first and then turn their attention on Japan.
Attacking Germany in 1942 would be disastrous. The goal was to "contract" the German empire. The Americans and the British identified the "soft underbelly" of the empire. The US would attack Germany by going after the weakest part = Italy.
"Island Hopping" = In Asia, Japan controlled the seas and thus, the war in Asia was a Naval campaign with Marines serving as ground troops. Attacking mainland Japan was not an option in 1942. Therefore, the US had to painstakingly make their way toward Japan by taking the outlying islands...called "island hopping."
Japan is an island. Therefore, if the US could cut off their supply routes, the Japanese would run out of supplies in time. Additionally, no plane could reach Japan in 1942 from Hawaii. Taking the small islands allowed the US to set up airfield and supply depots. It would be a long campaign.