How did america's fortunes of war change during 1813 and early 1814, and what were the results of this change?

Throughout 1812 and 1813 (the earliest part of the War of 1812), the American military was terribly unorganized, undisciplined, and underfunded. They'd suffered huge, embarrassing losses (including the burning of what we now call the White House in Washington). But by 1814, the circumstances of the American Army had changed drastically. After a number of failed campaigns and territorial losses, the Americans finally had a major victory in late 1813, at the Battle of Lake Eerie.

This naval battle, which took place in September, saw the American commander Oliver Perry lead his forces to a decisive victory. Not only did the Americans gain a much-needed boost in morale only a month after the burning of the White House, but they also gained control of Lake Eerie (an extremely important waterway) and drove British forces out of Detroit (also a major waterway and an important navigation point on the Great Lakes).

Most importantly, American control of these waterways cut British troops off from their Native American allies in the west, whom the British could now no longer resupply with weapons and ammunition. For these reasons, those Native fighters mostly dropped out of the war, which was an immense relief to the United States and signaled a key turning point in the war.

In short, you could say the difference between 1813 and early 1814 was like night and day for the Americans.