[ios] How do I detect when someone shakes an iPhone?

You need to check the accelerometer via accelerometer:didAccelerate: method which is part of the UIAccelerometerDelegate protocol and check whether the values go over a threshold for the amount of movement needed for a shake.

There is decent sample code in the accelerometer:didAccelerate: method right at the bottom of AppController.m in the GLPaint example which is available on the iPhone developer site.