How are NFL stadiums actually funded, and what is the economic impact on the city/state?

With the recent announcement about the Kansas City Chiefs moving from Missouri to Kansas, there’s a lot of discussion on Reddit about how NFL stadiums (and stadiums in general, I guess) get paid for. Some people say “taxpayers are footing the bill for these stadiums,” but the results of my brief research into the topic seemed to revolve around bonds and sales tax recoupment, and so I’m thinking it is not really “free public money” in the same way people are perceiving?

Can someone explain the general economic process for when a city or state is financially involved with stadium development? And are there any studies about the economic impact of: a) public funding assistance for stadium construction, and b) long-term benefits of stadiums being present in a state/municipality?