iPhone does not Ring

There are 2 things you need to check:
#1- Be sure the switch on the side is flipped forward (you'll see a red mark beside the switch if it's flipped backwards), and
#2- Press the + sign button that's under the switch to increase the volume. (if your phone is locked you won't see the volume increasing, so unlock it so you can).

#2 is likely the problem.

That also increases the sound of the alarm, etc.