My phone does not ring when a call comes in. It just vibrates

I'm sorry if this sounds like a dumb response, but make sure you have your ringer on and your phone isn't on silent. If that isn't the reason, go to Settings > Sounds, and slide the Ringer and Alerts volume slider to a volume you'd like.

Check the mute switch along the edge, near the external volume controls. Orange showing = muted (vibrate mode).