What were the goals for progressives and how did they hope to achieve these goals

Some of the goals was to break up business monopolies, regulation of railroads, introduced referendums for voters to initiate laws, etc.

The goals of the Progressives was to break up business monopolies, regulation of railroads, introduced referendums for voters to initiate laws, the election of the U.S. Senators by the people. and a graduated income tax. I think that is more than three, but you can choose from these!
Anyways, presidents Theodore Roosevelt and Woodrow Wilson were known as progressive enthusiasts. Various Congressional acts and constitutional amendments saw these concerns brought into American law.  :)

I really hope that this helps you