Do you get an assigned seat when you purchase the ticket? How does seating work?

No, generally first come first served. Occassionally some seats seem to be reserved. The seating layout varies from play to play.

First come first served

Just to add to the correct answer already given, it should be added that the Players Ring has no "bad" seats. It's a presentational space, and anywhere you sit turns out to be fine.

Previously answered