Short answers, pulled from the story.
The Second Party System was the political party framework operating in the United States from about 1828 to early 1854. It was defined by two major parties, the Democratic Party led by Andrew Jackson and the Whig Party assembled by Henry Clay, and is notable for producing the first well-organized national political parties in American history.
Jackson won more popular votes and more electoral votes than any other candidate in 1824, yet the House of Representatives chose John Quincy Adams as president. Adams immediately appointed Henry Clay as Secretary of State, which Jackson publicly denounced as a "corrupt bargain" between Adams and Clay.
The Specie Circular, issued in July 1836, declared that federal land could no longer be purchased with paper money issued by banks; only gold and silver coins were accepted. Most businessmen and bankers moved to the Whig party in response, while Jackson became more popular with subsistence farmers and day laborers who distrusted finance.
On the Democratic side the major figures were Andrew Jackson, Martin Van Buren, John C. Calhoun, James K. Polk, Lewis Cass, and Stephen Douglas. On the Whig side they included John Quincy Adams, Henry Clay, Daniel Webster, William H. Seward, and Thurlow Weed.
The Whig Party collapsed because it could not agree on a position on slavery. As a coalition of Northern National Republicans and Southern Nullifiers who held opposing views on slavery, the party could only survive as long as the issue was kept off the agenda. By the early 1850s that was impossible, and the party disintegrated; after endorsing Millard Fillmore in 1856 and John Bell in 1860, it ceased to exist with the outbreak of the Civil War in 1861.
Martin Van Buren was Jackson's key political architect. He organized the Albany Regency in New York, one of the country's first successful statewide political machines, and brought Virginia and Pennsylvania's electoral votes to Jackson in 1828. Historian Robert Remini described Van Buren's creative contribution to the nation's political development as enormous, crediting him with arguing that the party system was the most intelligent way democratic affairs could be conducted.