Hamilton was born in 1757 in the West Indies, and was orphaned at the age of 11. However, his cleverness showed early, and his employers pooled their money to send him to university. Either that, or they just wanted him out of the building. Hamilton moved to New York in 1773 and began attending King's College (later Columbia University). By 1774, he was writing pro-rebel articles - not really in the spirit of attending somewhere named after the King - and by 1775 he'd joined the volunteer militia. Again... probably not exactly what his sponsors had in mind when they sent him there.
Hamilton fought during the occupation of New York in 1776. He was a natural leader, and George Washington appointed him an aide-de-camp - a job he held for 5 years. However, Hamilton was eager to get back into battle and in 1781 he commanded troops during the decisive victory at Yorktown.
Hamilton became a member of Congress for New York in 1788. He developed a particular fixation on the funding of the Federal Government, which at the time was... well, broke, as it wasn't allowed to demand any taxes from the member states. (While that may sound wonderful when you're looking at your federal tax bill, it meant the government couldn't do thing like pay their army. Soldiers like getting paid.)
In 1787, Hamilton was named the first Secretary of the Treasury, where he fought for a strong federal government (in heated opposition with Thomas Jefferson, who promoted states rights). Hamilton was responsible for creating much of the foundation of the US Fiscal policy, the details of which are probably important, but so indescribably boring I can can barely be bothered even to finish this sentence.
But I did. Because I care.