What were the main political issues during the Gilded Age (1877–1900)?

There were a number of major political issues during the Gilded Age, which was once characterized as a period of factional maneuvering without an ideological basis. Many of these issues pitted establishment politicians in both parties against a group of reformers led by agrarian politicians from the West in particular.

One important issue was the tariff. Banking interests and American manufacturers desired a high tariff, while agriculturalists and many ordinary Americans did not. This old debate in American history became particularly intense during this period, because high tariffs basically favored manufacturers with artificially inflated prices. Debates over currency, or monetary policy, broke along similar lines. Many ordinary Americans, especially farmers, wanted more money in circulation, while financiers and business interests favored the contractionary monetary policy that characterized the post-Civil War period.

Another major (related) issue that became political was how the government should deal with the powerful monopolies that came to dominate the American economy. Regulating the monopolies was a major campaign issue for Populist politicians, who advocated government control of railroads and telegraph companies, for example. Some other politicians were already advocating the breakup of large monopolies, and the Sherman Anti-Trust Act of 1890 was passed by Congress to this end.

Other major issues included civil service reform, a movement that took place in both major parties. This was seen as a means of fighting the corruption and malfeasance that characterized the politics of the period, from the municipal to the national level. Immigration was also an important issue. Many Americans advocated for immigration restrictions, especially in the American West. This led to one of the most flagrantly discriminatory federal laws in the history of the nation, the Chinese Exclusion Act of 1882.

Probably the most important political issue of this period was the issue of the gold standard versus free silver.  This pitted business interests against farmers.  The farmers wanted silver money to be coined so that the value of the dollar would decline and it would be easier for them to pay off their loans.  Business interests wanted a strong and stable currency.  This issue played out over a number of presidential elections.

A second important issue was the issue of regulation of railroads and other major utilities.  This was another major issue for populists.  The populists (mainly farmers) wanted the government to regulate railroads because the farmers needed the railroads to get their crops to market.  Because of this, the railroads could charge very high prices to farmers.  The farmers felt that they were being unfairly exploited and wanted the government to prevent this.

These were the two most important political issues of the time you are asking about.

Who were the significant political figures, parties, and factions of the Gilded Age? Why is this era called "gilded" and which issue was most effectively addressed by the US government?

The Gilded Age refers to the last third of the nineteenth century in the United States. The term derives from a novel of that title by Mark Twain. This era of American history is referred to as “gilded” because of the great wealth acquired by the few and their ostentatious display of their acquisitions. Gilded means that gold has been applied to the exterior of an object. To call something gilded implies that its attractive qualities are superficial or even misleading, as contrasted to something that is solid gold, or authentic.

One of the most important issues of the era was the virtually unchecked amassing of tremendous wealth by a handful of industrialists. These ultra-rich men—a group that included Carnegie, Rockefeller, and Vanderbilt—are often derogatorily called the robber barons. They accumulated tremendous power along with their fortunes by holding monopolies in commodities such as oil and steel and by controlling the closely related transportation industries. The government role in addressing this issue was fairly successful. Trust-busting, or the breaking up of monopolies, was partially achieved by the Sherman Antitrust Act of 1890 and the related Clayton Act of 1914.