A piezoelectric ceramic element is a sintered body of many crystals (poly-crystals).  Distortion of this crystal occurs when a stress is applied to the element either thermally, mechanically or electrically. For piezo sounder applications a metal plate is typically attached to the ceramic element and it is this plate which vibrates due to the expansion and contraction of the piezo ceramic the resonant frequency of the ceramic is too high to produce an audible tone directly itself).

Be sure that your device is really a piezo, and not magnetic(measure its resistance!)

Piezo pro's:

Low power (they have an impedance of meghoms and therefore require next to no current to drive them)
They require a voltage to excite the piezo material but it can be as low as 1.5V.
They make a lot of noise when you hit their resonant frequency.

Piezo Con's:

They require being pulsed at their resonant frequency (ie if it's a 2.4kHz piezo it needs to be driven at 2.4kHz
If you don't give them with their desired frequency their volume is rubbish.

Driving

You often need to drive a piezo sounder (assuming it has no internal electronics) in a push pull fashion to get a high volume – i.e. the 2 pins flip polarity at the required frequency. You often can't simply give it a PWM signal on 1 pin with the other connected to 0V or +V.  This is not necessarily the case for "piezo buzzers" (which draw more current).

Square wave driving is usually fine up to about 30V.  If the square wave voltage is higher then there is a good chance for shockwave, damage, cracking, reduced life, or other failures. In this case there needs to be careful control of the  rise and fall times of the drive voltage.

Are Piezo Sounders Inductive?

Yes but piezo sounders are largely capacitive (as opposed to buzzers which are inductive).

Can a piezo be left powered in one drive state

I.e. can you leave 1 pin at +V and the other at 0V?  No, in order to prevent depolarization of the ceramic elements you must ensure that the piezo is not powered with direct current (DC).

Reducing The Volume of A Piezo

Reduce the driving voltage.

Use a sine wave instead of a square wave.

Connecting a parallel capacitor across a piezo sounder will reduce the volume if using a square wave to drive it, as the sharp edges which give the maximum sound outputs will be rounded off a bit.

Piezo Drive Circuits

Nifty 2 transistor 5V drive from a single PWM pin.

Good driver IC's

MIC4225