If you have the TodayTix app, you can enter their lottery. There's also a virtual lottery on the Public Theatre website, and there's an in-person lottery at the Public. They start taking names at 11:30 AM and draw names at noon. If none of those work out for you, there's always the cancellation line at the Delacorte. I'm not sure how early people are lining up for cancellation tickets these days, but it's worth a shot. When I saw it, I got to the line around 5:45 and still got a ticket. (Of course, there were rumors of a rainstorm that night, so that's probably why the line was so short. That would have been perfect weather for The Tempest if you ask me!)
"I have maggots in my scrotum!"