Eric Slivka at MacRumors notes that Apple Music senior director Ian Rogers made a revealing blog post this weekend, announcing the launch times for iOS 8.4 and the Beats 1 "radio station" on Tuesday, June 30. iOS 8.4 is expected to show up at 8 AM PT, with Beats 1 going live an hour later at 9 AM PT.
Rogers discussed his life in music in the post, saying then that "Tuesday morning we’ll be unveiling the next chapter. Please make a note to upgrade to iOS 8.4 at 8am PT Tuesday, June 30th and listen to the first Beats 1 broadcast at 9am PT. Here’s a Facebook invite to make it easy for you to say yes, you’ll be there, and invite all your friends. See you there."
For the update, you can either obsessively check Settings > General > Software Update starting at 8 AM Pacific Time, or wait for the notification to arrive. Remembering last year's debacle with an update that bricked iPhones before it was quickly pulled, you may wish to wait a little bit to see if any early adopters are having issues before updating your devices.