Q: Previous versions of iOS had a feature where one could double tap the home button on the home screen to access music controls. How does this work on iOS 7?

– Joshua
A: All of these functions have been moved to the new iOS 7 Control Center which can be accessed by swiping up from the bottom of any screen—including the lock screen—subject to your preferences set under the Control Center section in the iOS Settings app.
Double-tapping the Home button from the home screen has not actually provided direct access to music controls since prior to iOS 4.0—the point at which the recent apps tray appeared and those controls were moved to that location. Access to music controls in iOS 4, 5, and 6 therefore required multiple actions—a double-click of the home button followed by a left-to-right swipe gesture on the recent apps tray to switch over to those controls. The Control Center comes up with a single upward swipe gesture and provides direct access to not only music controls, but a number of other commonly used features.

On the iOS 7 lock screen, playback controls are now displayed automatically, without a double-tap of the Home button needed to bring them up. A triple-tap single tap of the Home button will temporarily return the standard clock view in case you need to see the time (thanks to Larry for pointing out in the comments that only a single-tap is actually required now).
Be sure to check out our complete guide to the Secrets & Features of iOS 7 for the full run-down on what’s new and different.