How does a solenoid work to mack a doorbell ring"?

When a current goes through the coil (solenoid), because someone pushed the on, a magnetic field is created which attracts the "hammer" that hits the bell. The hammer is normally closing a contact. As the hammer gets away from the coil, the contact gets open and the current stops flowing through the coil. The hammer then returns to its original position (because of spring action), and the cycle repeats again and again.