A. Everyone thinks the US currency dollar is so powerful and the country is so powerful and hence 'Dollar' is the global bench mark. This is not true entirely. Consider yourself, going anywhere in India, you can live, buy and sell etc because we have a single currency that is accepted in all states.
B.Now, enlarge the picture to the global scale, the world needed a system of exchange that can be agreed by others so that it is easy to buy,sell,lend,borrow and basically do everything you do at a much large scale.
C.It all looks easy now, but if you wind the clock back to the period around the world war II, a significant milestone was achieved at the 'UNITED NATIONAL MONETARY AND FINANCIAL CONFERENCE' at Bretton Woods, New Hampshire ( 1st-22nd July 1944).
At this meeting, the world leaders decided to equate the currency of a country to the price of gold. In this situation, the US dollar became the resevre currency linked to the price of gold.
D. It is widely felt that Harry Dexter White, the chief international economist of the Treasury Department, out performed his counterpart(Mr.John Maynard Keynes) from UK. The Bretton Woods system came into vogue in 1958, where in suddenly all the world's currencies became 'convertible'. Every trading nation started converting, managing and settling it's trade accounts in US dollars and US dollars in turn were fully convertible to gold.
E. At the same time, the Bretton Woods agreement paved the way for the origin of 'INTERNATIONAL MONETARY FUND'(to lend the reserve currency- dollar to other nations in need) AND 'WORLD BANK GROUP' ( to provide financial assistance to the countries to re-shape the economy after the world war). Both these large organisations dealt with US dollars for helping the needy nations.
F. This, along with the good industrial growth, huge gold reserves and growing economy of USA in the post war period, led to the phenomenal raise of the power of the US dollar. SO much so that the strong dollar led to the collapse of the Bretton Woods agreement and unofficially the dollar replaced gold. This was also aided by the fact the combined growth of the world's economy outgrew the supply or reserve of gold.
G. So, USA with a strong economy, vast gold reserves, being a super-power and a world class military led the way for the US dollar to become popular and acceptable world over.