How do you find out if people trust or want to participate in polls? You poll them. Look, if you have a better suggestion, I'm sure the pollsters would love to hear it.
Kantar, a U.K.-based research firm, conducted a survey to find out what people think of...surveys. They don't much like them, it turns out! Seventy-five percent of Americans (Kantar only talked to Americans) think political polls are biased in some way. Seven percent think they're biased in favor of conservatives, 11 percent think they're biased in favor of liberals, and the remaining 57 percent don't quite know how they're biased, but are still pretty sure they are. That skepticism isn't unreasonable; bias in a statistical sense doesn't have to be intentional. It could merely be an inaccuracy introduced by an unintentionally skewed sample, or imprecise wording of questions, or all kinds of other things.
The types of polls Americans do trust--at least, what the people polled say they trust--are nonpartisan, from academic organizations or otherwise unaffiliated groups. Polling companies like Pew and Gallup are not trusted as much as nonpartisan groups, nor are polls from news organizations like the New York Times and USA Today. Internal polling, from a candidate or political party, is hardly trusted at all, and 23 percent of respondents say they wouldn't even participate in an internal poll.
There are some curious findings about how effective various polling methods are: 60 percent of respondents say they wouldn't participate in a poll on a social media site, for example, which could heavily skew the results to over-represent the kind of person who would participate (which might be a younger or might be an older audience, who knows). The poll also drives home the increasingly difficult problem that more and more Americans rely on cellphones as their main or sole phone, and that it's both harder and viewed as more intrusive to poll via a cellphone.
Anyway, you can read the whole Kantar report here.