The new 9.0.1 update can be downloaded over-the-air through the Settings app on the Apple TV by going to System –> Software Update.
tvOS 9.0.1 comes as Apple is testing the first major update to the operating system, tvOS 9.1. Apple has thus far seeded one beta of tvOS 9.1 to developers, with release notes for that beta pointing towards improvements to networking and scrolling. tvOS 9.1 also appears to include support for Siri search for Apple Music.
Any noticeable changes found in the OS will be listed here as part of updates.