When a voltage is applied across a piezoelectric crystal, the crystal expands and then contracts again. By connecting the crystal to the sound output of a device where a normal speaker would usually go, a radio's output for example (see diagram below), then the device will supply a varying voltage and the crystal's expansion and contraction will produce sounds waves. You now have a speaker!
Stepping up the voltage to the piezo crystal with a transformer
If the voltage coming from the source device isn't high enough then you can step it up with a transformer. Unless you design a transformer specifically for radio frequencies then this won't be ideal, but it does work.
Stepping up the voltage with a doorbell transformer
I first tried a doorbell transformer (see photos below), ones normally used to convert 120V to 12V (for example) for powering a doorbell from household power. Simply wire it backwards, the 12V side to the device's output and the 120V side to the piezoelectric crystal. In my case, my transformer had two 6V options so I used one of those instead.
Of course the signal from the radio isn't 6V and the output from the transformer isn't going to be 120V. I'm just using the transformer for it's ability to step up voltages, in this case the radio's output voltage.
Using the doorbell transformer made a significant improvement in the speaker's volume over no transformer at all.
Doorbell transformers are available wherever household electrical supplies are sold.
Stepping up the voltage with a microwave oven transformer
If the sound from the crystal is still too quiet then you can try increasing it with a microwave oven transformer instead (see photos and diagrams below.) This gave me a big improvement. These transformers can easily be scavanged from old microwave ovens.
The tricky part was that the output coil has only one wire lead coming off it. I'm assuming that the other end of the coil is connected to the transformer case. So for the other output I connected one of the inputs from the radio to the case and took the other output from the case, treating that side as if it were ground, even though the radio has no ground.
Using the microwave oven transformer made a significant improvement in volume over the doorbell transformer.
WARNING: Be very careful taking apart a microwave oven. There is a high voltage capacitor in it that may still be charged. Do some homework first.
Different piezoelectric crystals you can use
Paper cone piezo speakers with various diaphragm materials
I also experimented with making speakers using paper cones, with the aim of making a good earpiece that would channel the sound into your ear. I tried with an aluminum foil diaphragm but it was to hard to keep it stiff. A paper diaphragm stayed stiff but an aluminum flashing diaphragm gave louder sound. I found that the sound from these was much clearer than the above speaker made from a can. The volume was less though.
Videos for piezoelectric speakers
This video shows my experimenting starting with no transformer, then the doorbell transformer and finally, the microwave oven transformer. It also shows various piezoelectric crystals I tried, as well as some different speaker configurations.
This video is of me showing that a small rochelle salt crystal works too and how a window can be used as the speaker diaphragm with loud results.