How did Progressive reform make the government more democratic? I'm studying federal reforms like amendments and state reforms like initiatives,...

The American
Progressive movement is generally considered to have originated in the late nineteenth century
as a reaction to the abuses of big business and the problems that plagued the lower
socio-economic classes of that era. 

The first post to this question gave
some of the electoral reforms enacted by progressives. The movement as a whole could be
considered democratic in the sense that it was concerned with helping the little guys who
could not help themselves. So progressives took on government and big business, often in the
form of increased regulation, to help make it more responsive to the needs of people in
general. Many people feel that this movement led to Roosevelt's implementation of the New Deal
during the Depression.

In modern America we see the influence of
Progressivism in movements like Occupy Wall Street, which seek to limit the power and influence
of big business.

Some consider Donald Trump to be a progressive in some ways.
His call to help American workers by encouraging businesses to stop exporting their jobs abroad
is progressive in the sense that it uses governmental power to influence business for the
benefit of common Americans. Whether or not this will actually work to America's advantage
remains to be seen. Trump, however, is decidedly not progressive in other ways, such as his
attitude toward immigration and business regulation.