Basically, when did the US become a "world power," or when did the US start to have a large influence on world affairs? Also, why did it happen when it did?
Economically, the United States was a superpower already before 1914. America's was first noticed on a 'hard power' level when they defeated the Spanish in 1898 and acquired the Phillipines. Afterwards, they steadily became more and more influental, mainly in South America, for example by building the panama canal. Teddy Roosevelt, ruling in the early 1900's, called their policy: 'walk softly, and carry a big stick'.
The soft walking changed to marching in WW1. The United State's suddenly became a world class player after when the U.S army had a key role in defeating the Germans at the end of WW1.
The old, aristocratic order of Europe had failed itself. The United States now had a 'soft power' card to play: 'to make the world safe for democrasy'. This was appeasing to europeans, and now the U.S could play, next to their economic might, ideologically, a leading role.
Most historians would say the [great white fleet] (http://en.wikipedia.org/wiki/Great_White_Fleet) was the United States' coming out party as a world power.
Theodore Roosevelt, briefly Assistant Secretary of the Navy during McKinley's first term, accelerated the buildup of naval forces during his presidency. In 1907 he sent an American battle fleet of 16 battleships and their support craft on a two year worldwide "goodwill" tour. The stated intent was to "give the navy practice in navigation, communication, coal consumption and fleet maneuvering" (shamelessly plagiarized from wikipedia), but it was really an extension of TR's "big stick" diplomacy.
I think the ascendency of the United States comes broadly in three stages, obviously supported by the general growth of the US economy and population in between.
The first transition comes at the end of 1898 in the Spanish-American War. Until this point, the United States had been largely an inward-focused and militarily unimpressed nation, given its size. Sure, the US sent an expedition to Korea, opened up Japan with a gunboat, and participated briefly in the Opium Wars with Britain -- but these were all at the direct behest or with the implicit approval of more powerful European nations.
In 1898, the United States defeats a European power by itself for the first time. This, in my mind, marks the moment when the United States ascends to 'regional power' player -- the US wasn't going to go sucking up colonies in Africa, but it was affirmed as a dominant power in it's locale.
Then in 1918, the order is shaken up, and several great powers of Europe bite the dust due to World War I. In this vacuum, the US takes a seat at the Great Power table, along with Britain, France, Russia, Germany, Japan, Italy. Notice anything?
Yes, these are the principal players of World War II. After the re-shuffling that occurs in the Second World War, the United States and the Soviet Union emerge as the dominant superpowers.