In my experience, backstage tours usually come about in 1 of 3 ways: through school programs, premium show tickets, or you need to have a personal connection to someone who works in a show. I've managed to get backstage tours of several shows, but only because I had a professor who set me up with a connection. Premium ticket holders (depending on the show) get to go backstage. I remember Spider-Man: Turn Off The Dark offered backstage tours to audience members who were willing to pay $300 for a premium seat to the show. The only tour that I'm aware of that is open to the public (and at an expense of only $30) is Wicked's 'Behind the Emerald Curtain' series which is held at 10am on select Saturdays in the Gershwin Theatre. Usually two members of the cast show you costumes and the set model before you go into the theatre itself and sit down for a video presentation.
"Mostly, I loved the size of these people's emotions. Nobody has emotions this size anymore. Outsized emotions. Operatic emotions. Kushemski and Vanda are like Tristan and Isolde, they're Paolo and Francesca. Nobody's in total thrall like this anymore. Nobody's overcome by passion like this, or goes through this kind of rage." Thomas, Venus in Fur