In what ways was the American political system democratized between 1789 and 1877?

There were various ways that the American political system became more democratized between 1789-1877. In the early days of the United States, only male property owners were allowed to vote. This requirement began to disappear in the 1800s. Between 1824 and 1828, the percentage of white males who voted increased from 26.9% to 57.6% in part because the property ownership requirement was dropped in many states. Over 80% of white males also voted in the election for president in 1840.
Another change that occurred was that party's members instead of the party's leaders chose the candidates for office. Prior to this switch, party caucuses, run by the party's leaders, were used to choose the candidates. Eventually, nominating conventions were used to choose these candidates. With this scenario, the party's members chose the candidates who would run for office. Additionally, people began to choose the electors to the Electoral College instead of having the state legislature choose them.
When Andrew Jackson became president, he began to give government jobs to common people. The use of the spoils system, which was the practice of giving government jobs to one’s political supporters, helped to break the hold that the upper class had on these government jobs.
After the Civil War, the Fifteenth Amendment was passed. This amendment made it illegal to deny voting rights based on a person’s race, color, or if that person had been a slave. This allowed more African American males to not only vote but to also run for office.

The American political systems were democratized in this time period as more people got the right to vote and more people became interested in politics.  Between 1789 and 1824, many states lowered the property requirements to vote or abolished them altogether.  By allowing more poor voters into the process, candidates often had to appeal to them in basic ways.  Candidates from this period often did not make public appearances for themselves, but campaign managers held barbecues and issued campaign buttons for their respective candidates.  It was also important for the presidential candidates to appear to be regular people—Abraham Lincoln was portrayed as a frontier rail-splitter even though he was one of the most successful patent lawyers in Illinois when he began his presidential run.  William Henry Harrison was portrayed as someone who began life in a log cabin and enjoyed a jug of hard cider on the porch when, in reality, he was one of the richest farmers in Ohio.  At the local level, city bosses catered to immigrant communities whether or not they were naturalized citizens.  This led to corruption especially in places like New York City which was run by Tammany Hall immediately after the Civil War.  
The Civil War also brought African Americans the right to vote with the Fifteenth Amendment in 1870.  Radical Republicans passed this measure while much of the South was not admitted into the Union.  This opened the door for many educated African Americans to seek office in Congress at the state and municipal level. However, African American political participation would drop severely at the end of the Reconstruction period in 1877 because whites in the South tried to regain the status quo through a series of literacy tests and poll taxes meant to keep black people away from the polls.