How did populism offer an alternative to the traditional two parties of Democrat or Republican? Do you still see some elements of populism in politics today?

Populism is going by what will improve the lives of everyday people (typically people in the middle or lower class), such as lower taxes, lower gas prices, lower unemployment, more economic opportunities, etc.. Populism is somewhat of a blanket term used to describe what ordinary people generally want/need to survive.

The Republican and Democratic parties do not typically create policies over what ordinary people want or need. Additionally, the two parties are generally run by elites or lifelong politicians. They typically have an agenda that they push politicians in their respective parties to follow, regardless of what the people want at a give time. There are exceptions, and their agendas are somewhat influenced by what their bases want to see from them, but generally they put priority on their agenda over the people's concerns. Their agendas are much more political, catering more to their respective parties over what the majority of the country would agree on.

Populism is an alternative in that its goal is to solve the issues that everyday citizens are worried about. Like stated earlier, this generally includes job security, and better economic prospects. Additionally, populism favors ordinary people regardless of their political leanings. It pulls policies or ideas from both right and left to create policies that will hopefully benefit the majority of citizens.

Populism is once again gaining traction in the US even as more and more non-politician candidates are in the running for office, promising to improve the lives of their constituents (mainly through economic means) while not interfering with their lives or beliefs as much as possible.