I think you caschw is describing a soft-reset.
Windows Phone 8 hard-reset goes like this:
- Turn off your phone.
- Hold volume-down.
- Keep holding volume-down and press power button for about 3 seconds.
- Let go of the power button, but keep holding the volume down until image/icon on the screen appears.
Almost done - now proceed with the following sequence:
- Let go of holding the volume-down and press:
That kicks the phone into a hard-reset sequence, which should take about 40-60 seconds.
If you did all of that correctly, the phone will take you to the "Welcome to your Windows Phone, let's get started screen."