The rise of the United States as a dominant power covers a long period of time, so I'll just give a relatively brief summary of the events that lead up to it. Also, this is by no means comprehensive, as there were multiple powers (pre-1871 Prussia, the Russian Empire and Austria) that came close to rivalling the major dominant powers.

For most of modern and early modern history, world politics were largely dominated by the Anglo-French rivalry. Though their relative power, both to one another and to other major powers fluctuated, they were the main world powers. Britain, through their naval supremacy, controlled the seas and therefore the largest colonial Empire while France was the leading power on the European continent, especially under Louix XIV and Napoleon I. There is a reason why the two periods of time that more or less coincided with the lead up to WW1 are popularly called the Napoleonic period (after French emperor Napoleon) and the Victorian period (after Queen Victoria of the United Kingdom).

When the German coalition under Prussian leadership decisively crushed France in 1871 during the Franco-Prussian war, the newly united country of Germany established itself as a major power and soon established its own colonial empire that rapidly became the third largest after the UK and France. By this time, the United States was one of the most industrialised countries and a huge economic powerhouse, but it was far from a military power yet. When the United States joined World War One in 1917, their military was largely underdeveloped and a large part of their materiel, most importantly tanks and machine guns, were supplied by the UK and France. United States 'doughboys', as the American troops were cold, famously used British Brody helmets (apart from the Harlem Hellfighters, who used French Adrian helmets) and French Renault FT tanks and Chauchat light machine guns. From 1914 to 1917, the Americans were officially neutral, but supported the Entente powers of France, UK and Russia through their sophisticated industry, which helped further establish the US as a major centre of wealth and industry. Conversely, WW1 pushed the European economies to their absolute limit. The UK, France and Germany suffered 8.8, 8.6 and 13.2 million casualties against 4.4 million for the US. Considering that the US is several times larger than any of the other countries, the US economy came out on top.

This is where the balance of power starts to shift and the United States starts to be considered as a major power in international politics. However, WW1 also marked the point where both the British and the French empires were at their absolute peak, since they gained mandates to govern parts of the Middle-East from the League of Nations, and also split the former German colonies among them. Though Germany was crushed, it also managed to recover surprisingly quickly and covertly developed a military machine that would crush its main rival in France with surprising speed in 1940. Historians Ian Sumner and François Vauvillier note that in 1939, before the invasion of France, the French army was still believed to be the most advanced and the most powerful. Why Germany managed to so quickly defeat France is a whole different topic that I won't get into now.

World War II is what marked the true beginning of American hegemony. Europe was largely left ruined after both World Wars and the end of the war coincides with various decolonisation movements that, for obvious reasons, affected UK and France the most. Meanwhile, the Soviet Union had emerged as a rival to the US, both in might and in influence.

I'll stop here because I feel you're likely familiar with the more contemporary post-WW2 and Cold War history.

TL;DR: The end of WW1 established the US as a major power, and the end of WW2 established the US as the major power alongside the USSR. The fall of the USSR in 1991 meant that the US was the main powerbroker in the world.

Hope any of this is useful.

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Sources (among others):

Sumner, I. Vauvillier, F. (1998) The French Army of 1939-1945Paddy Griffith (1998).

The Art of War of Revolutionary France, 1789–1802

Chamberlain, M.E. (2014) The scramble for Africa

James, L. (1994) The Rise and Fall of the British Empire