People supported Manifest Destiny because they believed that the land was theirs. They believed in growth for their country. Manifest Destiny pretty much meant that the people of the United States thought, we are the best. We deserve this land. This is ours, and we are going to take it. And that is exactly what they did. The United States took every chance they got to snatch up as much land as they could, and that resulted in a big growing nation.
At the end if the Revolutionary War in 1783, the British gave America control of enough extra land that America doubled in size right away. Then the United States stumbled upon a chance to buy some extra land from France. For an amazing low price in 1803 America doubled its size again. The land was sold to the U.S by Napoleon Bonaparte. This is known as the Louisiana purchase. The U.S had then spread halfway across the continent. Then for a few decades, growth basically stopped. But then by the 1840s, more and more American settlers were moving west, and many United States leaders were itching to get their hands on more territory. The United States picked up some more land here and there by negotiating with European countries that controlled land near by.
But then there was Texas. There, American settlers had won independence from Mexico in 1836 and asked to become a part of the United States. Then Texas became a state. By that time, the American hunger for more territory had grown pretty intense. The tensions between Mexico and America had grown too, and Mexico owned most of the land between America and the Pacific Ocean. There was then a war with Mexico and America won. Many citizens from Mexico that were living on the land that was fought for were pushed out by settlers. Around the same time, America worked out a deal with Great Britain to get the Oregon territory. By the end of the 1840s, the United States had stretched from coast to coast. Settlers then started pouring into the new western frontier.