It seems to me that populist politicians exploit the legitimate grievances of ordinary people, particularly the disadvantaged, by pointing the finger of blame at "elites" or "immigrants" or "foriegners" or even sections of these disadvantaged themselves such as "benefit claimants".
The key to getting votes for populist parties is, firstly whipping up feelings of anger and resentment, secondly targetting those to be held responsible (whether they actually are or not) and, most importantly, offering very simple answers to very complicated questions - you vote for us, we'll get out of the EU/ deport all asylum seekers / slash foriegn aid / cut the benefits of scroungers/ build more prisons/ bring back hanging / cut taxes etc.
They will not usually offer up all these wonderful policies at once, as it could confuse the voters, so to keep it simple, start with just one thing, say leave the EU, then make it "no-deal - WTO terms" and only if that is successful might other policies come along later. The key to success for populism is KEEP IT SIMPLE.