Essentially there were two competing strategies at the beginning of the war: from the army and the navy.

The theory was essentially an application of Alfred Thayer Mahan's theory of sea power. He believed in a network of ports for resupply to maintain direct lines of communication between the ports. It's similar to a land-based theory involving connected fortifications, except power is projected on sea.

In 1909 Homer Lea wrote an extremely important book The Valor of Ignorance. (Which you can find on Google Books. VERY fascinating read). He was worried, as many strategists were, about a growing Japanese empire after their beating the Russians in the Russo-Japanese War of 1904. He predicted, very accurately, how the Japanese would build a Mahanian influenced network of naval bases in the south Pacific to insulate themselves from attack. He was extremely prescient. A main point was that the straight between Japan and the Philippines was the lifeline for Japan. So, their first phase of the war was to conquer the Philippines in very short order (he even accurately predicted which beaches they would land on)

Throughout the first quarter of the 20th century, the Department of War Joint Army and Navy Board (the predecessor to the Joint Chiefs of Staff) began writing out a bunch of theoretical war plans that were color coded. i.e., War Plan Green was an invasion of Mexico, War Plan Red was for war vs. England (which was a chemical attack on Toronto, conquest of Canada, then naval blockage of the United Kingdom to starve them into suing for peace). The war plan against Japan was Orange.

Orange was an island hopping campaign. However, at the time of writing, it wasn't believed that aircraft nor submarines would be a major threat to big fleets. So, they only looked at islands capable of housing battleships and ignored islands only large enough for submarine pens or air bases. The three critical islands were Hawaii, Guam, and the Philippines.

Following the British's disastrous amphibious landing at Gallipoli in WWI, the US Marine Corps undertook the study of the amphibious landing. In 1920, Marine Major Earl Ellis was tasked with the study of amphibious landings and the South Pacific. He worked tirelessly and in 1921 published the Marine Corps manual Advanced Base Operations in Micronesia. It was the first ever attempt at an amphibious assault doctrine and strategy. Ellis foresaw the coming significance of air planes and submarines, so he added onto the Joint Board's War Plan Orange the Caroline, Marianas, and Pelew Islands.

So that was how it was executed.

During planning, the two major camps were the army and navy members of the Joint Board. As should be expected, the Navy favored the island hopping campaign that relied on naval power, and the Army favored a plan of a land battle on the Philippines to prevent it from capture and landing a couple armies on the Philippines as reinforcements. The big problem with the Army's plan was that the Washington Naval Conference in 1921 (an arms control treaty between America, England, and the Japanese) limited the fortification of the Philippines to the status quo. They weren't allowed to build any big concrete bunkers or house an extra couple hundred thousand men. So, when the Japanese landed in the Philippines, it was a short battle (and a decisive Japanese victory) and the island hopping campaign to take it back began.

Seversky's famous "Victory Through Air Power" posited that it would be entirely unnecessary to invade any islands at all with the proper application of air power. The Japanese empire was portrayed in the animated version of his book as an octopus whose tentacles would recede naturally if we attacked the main body. Seversky envisioned what would ultimately become intercontinental strategic bombers to get the job done.