A monomorph (the disk portion of a ceramic transducer of which you speak) is excited largely by the dV/dT of the driving signal - that is, it being a capacitor, it is the sudden change in voltage across the device that will cause the most current to flow and the mechanical effect. An emitter follower, by its nature, may (or may not) provide this when presented with the potentially large capacitance of one of these devices.
Many of these units are in cases with single-transistor driving circuits utilizing a small segment of the monomorph as a feedback loop - a sub-portion of the silvered surface that is electrically separated from the main: I've seen where people will mistakenly drive (or forget) that the piezo unit contains this circuit and drive it with an AC signal and get very little signal when, in fact, the unit as a whole was intended to be driven with a continuous DC signal for the contained oscillator circuit. It should be noted that the frequency of oscillation is partially set by the mechanical properties of the monomorph itself, but largely the resonant chamber consisting of the small air column above the monomorph and the small-ish hole from which the sound escapes - which is why the typical "sonalert" type unit without the internal driver circuit has such a limited frequency range over which usefully loud output may be obtained.
Driving a the "bare" monomorph directly is most easily done directly from the I/O pin of the processor itself: This is commonly done in the industry and is quite safe to do, even without a series limiting resistor. Much more output/drive may be obtained if you have two I/O pins available and can drive them in a complimentary fashion as this doubles the driving voltage.
Note that unless you use a specially designed piezoelectric "speaker" (rarely seen these days, but they used to show up in dial-up modems) their frequency range is going to be quite limited - typically in the 2+ kHz range.
If the advice of a large dV/dT signal (e.g. fast rise time such as a square wave) is heeded, they will make noise down into the Hz range, but as a series of clicks: As with the human voice, it will often not be the fundamental frequency that is perceived directly with these things, but the harmonics - until one gets into the kHz range - but the human ear and psychoacoustics being what they are, there may be the illusion - for some - of a wider range than that!
If you extracted the monomorph from an enclosure make sure that it did not get fractured due to (even slight!) bending: As you can imagine, this would render it practically inert - something that could be determined by measuring its capacitance: It should be in the many hundreds to tends of thousands of pF range, depending on the size. Finally, as you may have noticed, one driving terminal is the metal substrate on which the thin ceramic is mounted while the other is the silvered surface itself: If there is a separate feedback loop in addition to the main surface, the two (main and feedback) may be connected together.