I think that the best starting point is one suggested by Ross Douthat: populism is a "set of ideas [that] commands public support but lacks purchase in elite policy debate." It might seem that the exact nature of those ideas would be idiosyncratic--they would just be things on which there happened to be a gap between elite and pubic opinion at a particular place and time. However, there is a reasonably coherent set of ideas that meet this definition in most western nations since the end of the Second World War. One component is nationalism: the belief that nations have an obligation to think about their own people first and take care of problems "here at home" before worrying about the rest of the world. Reluctance to accept immigrants and suspicion of free trade follow from this. On foreign policy, the populist position is sometimes characterized as "isolationist," but it would be more accurate to say that it's impatient with diplomacy, international agreements, and long-term obligations: we should intervene when the nation's interests are at stake and then get out. On domestic policy, populism favors generous benefits to “deserving” people, like veterans, old people, and low-paid workers, but not general aid to the poor. It favors requiring companies (especially big companies) to offer good wages and benefits, and shifting the tax burden from individuals to corporations. It accepts ad-hoc intervention in the economy such as taking action against companies that make "excessive" profits. Finally, it's in favor of "law and order": it's impatient with protections for the rights of people accused of crimes, and doesn't have much interest in free speech for people with unpopular points of view. Why do I say that these are "populist" positions? Because they are all positions that are pretty popular among the public but are usually ignored or brushed aside in policy debates. On some of them it's a matter of degree: for example, elites are not against generous benefits to retired people, but they are more likely to say that demographic realities mean it will be necessary to raise the retirement age and cut benefits.
Advocating positions that are popular among the public might seem like a recipe for lasting political success, but Douthat says that populism has several forces that undermine it. One is "it often embraces bigotries and extremisms that in turn color the reception of its policies." That would limit its appeal, but it had already appeared in the campaign and didn't prevent Trump from staying close enough to win the presidential election, or Republicans from winning clear majorities in both houses of Congress. Another is incompetence and disregard for organization--that's definitely been on display over the last two weeks. A third is that elites unite against it. That would be the case in a healthy political culture, but the contemporary United States is not a healthy political culture: Trump has encountered only mild criticism from Republicans in Congress (“We all get disappointed from time to time,” Mr. McConnell said. “I think it is best to avoid criticizing them [judges] individually.”) Is there anything else that might hold a populist program back? Some populist policies might not remain popular if there were a serious attempt to implement them. For example, polls show a lot of support for an effort to deport all illegal immigrants, but if that actually happened there would be a lot of sympathetic cases, and support would probably decline. Populist economic policies would be likely to lead to recession and possibly to inflation or shortages. But it's unlikely that we will get to the point of implementing a populist economic program--Trump's administration seems to be divided, and almost all other Republicans are committed to cutting taxes and regulations on business--basically, an anti-populist program. So on economics, I think the Trump administration is likely to get the worst of both worlds--bad economic performance because of protectionism and ad-hoc intervention and bad publicity because of measures that appear to (and do) benefit business at the expense of the public.
[Thanks to Robert Biggert for discussion of these issues.]