Please explain the U.S. relationship with Britain prior to the War of 1812 and how the U.S. emerged victorious from that war.

America had a curious arrangement with Britain following the Treaty of Paris that ended the Revolutionary War in 1783.  Under the terms of the treaty, the British would evacuate the forts around the Great Lakes and America would control the territory to the Mississippi River.  After the war, more settlers moved into the region where they encountered stiff resistance, especially from the Shawnee tribe who were getting assistance from British soldiers who would not leave the region.  In 1795, John Jay went to Britain and negotiated more trading rights for Americans in the British West Indies.  However, Britain still occupied the western forts and still seized American sailors off ships in a practice called impressment in order to gain more sailors in its war with France.  It would be these seizures and the continued occupation of the forts that would lead to the War of 1812.  

The War of 1812 went disastrously for America.  Due to cuts in the military budget under Jefferson and Madison, America had little in the way of a navy to stop the British.  American militia was turned away in its attempt to conquer Canada.  The British burned the American capital in retaliation for America's burning of Toronto.  This war was really a sideshow of the greater Napoleonic Wars in Europe and the War Hawks in Congress (Calhoun, Clay, and Webster among them--you'll see these names again throughout the early 1800s) thought a war with Britain while they were distracted would lead to territorial gains for the young country.  America was able to end the war when the Napoleonic Wars ended for Britain and the British people did not want to stay involved in the conflict.  No territory changed hands, and the war does not get much coverage in history books today compared to other wars America fought.