How did the platform and ideas of the American Democratic Party change over time?
For the benefit of non-US readers, we have to remember that the United States has always been a two party system for all intents and purposes, so the best way to understand the Democratic Party is in relation to the other major party (which has changed over time) See generally The Formation of National Party Systems: Federalism and Party Competition in Canada, Great Britain, India, and the United States Pradeep Chhibber & Ken Kollman.
As a general rule, different issues that became important throughout American history changed the way parties defined themselves and their coalitions changed. Historians like to divide the United States into political eras divided by party systems, based on the dominant parties and issues of the period. William N. Chambers and Walter D. Burnham, eds. American Party Systems (1967).
In 1828 the Democratic Party was founded by the supporters of Andrew Jackson, and their opponents were the Whigs. Democrats opposed a national bank, the creation of corporate monopolies via the charter system, tariffs, and Whigs the opposite. Thus the Second Party System was created. Although both parties had support across class lines, Democrats in this period had the support of poorer farmers and middle class merchants, while industrialists and people tied to the broader commercial economy favored Republicans. Catholic Immigrants who were mostly poor supported the Democratic Party .During this period, both parties were competitive throughout the country. See The The Rise of American Democracy: Jefferson to Lincoln (2006), Wilnetz and , Political Parties and American Political Development: From the Age of Jackson to the Age of Lincoln (1992) Holt
Now, during the 1850's the Whigs collapsed as a political party because their Northern and Southern factions failed to agree to on a position on slavery while the Democratic Party supported the expansion of slavery in new territories. The newly founded Republican Party unified in opposition to the expansion of slavery. Thus the 3rd Party System was created. Let me emphasis how important slavery was to the 3rd party system , and it has implications that remain important to today. In 1860, when the Republicans had unified, this being their second presidential election, the party had no support in the South, but dominated in the North. The South was effectively lost to the Republican Party for the next 100 years as a result of the ensuing Civil War , hence the creation of the Solid (Democratic) South. In the North, the Democrats solidified their hold on Catholic Immigrants who feared that newly freed Blacks would travel North and drive down the wages of low-income earners such as themselves. Free Blacks in the North became loyal Republicans because of who they described as the "Great Liberator" Abraham Lincoln In the North, among Whites, class cleavages were still important as poorer Whites such as Catholic Immigrants were more likely to support the Democratic Party. Kleppner; Paul. The Third Electoral System 1853-1892: Parties, Voters, and Political Cultures (1979) and Foner; Eric Free Soil, Free Labor, Free Men: The Ideology of the Republican Party before the Civil War (1995).
I'll explain the 4th and 5th party system later, but this should give you a good idea how things started.