How did Progressives address the issues of big business, political rights, and social justice? How did they hope to bring about change?

is a long one,
starting roughly in 1865 after the Civil War and lasting until 1921 when Warren G. Harding took
over the Presidency and the 17th, 18th and 19th amendments had been added to the Constitution. 
The areas you include in your question are broad ones, but cover the efforts of the Progressive
Era pretty well in my opinion.  Building on the above posts, here are some additional thoughts
in those three areas:

Big Business: The main
effort was against the control of monopolies and trusts, groups of companies that controlled
entire industries and could therefore exploit both worker and consumer.  In the 1890s, the first
real piece of progressive legislation was passed in the Sherman Anti-Trust Act.  It wasn't very
effective as it was mainly used to break up unions, but it was a step.  Later, under Teddy
Roosevelt and especially William Howard Taft, the government became more progressive at breaking
these trusts apart (Standard Oil, 1912)

Political Rights:
The...