Typically you'll need two amplifier stages. A preamplifier to boost the "microphone" signal to audio line level (about 1V) and a power amplifier to drive the speaker.
You need to do some experiments... We don't know how much signal you're getting out of the piezo or the quality of the signal and we don't know how much amplifier power you need.
Do you have an oscilloscope? A multimeter? If the vibration is continuous you can measure the voltage from the piezo with your meter. If you've got short-duration "pluses" the meter won't respond quickly enough an you'll have to use trial-and-error unless you have an oscilloscope.
Or have you got a guitar amplifier? Piezos are high impedance and guitar inputs are high impedance, so it's pretty close to what you're looking for...
Your computer's soundcard has a microphone preamp. Try plugging the piezo into your computer and record it. The impedance of the mic input is too-low for a piezo and it will knock-down the signal. But if the vibrations & signal are strong enough, you may get something useful that you can listen to.
The next step would be to build a high-impedance preamp. You can build an amplifier (preamp) with [u]an op-amp and two resistors[/u]. A non-inverting amplifier like this naturally has high input impedance, and you'll need a 1M - 10M resistor from the + input to ground to "hold" the DC input/output at zero. Op-amps generally need plus and minus power supplies and you need 0.1uF bypass capacitors (phsyically-close to the chip) between the power supply connections and ground.
We have no idea how much gain you're going to need so you'll just have to experiment with resistor values. You may not need any voltage gain... You may just need a buffer (for it's high input impedance). That doesn't require any resistors (except for the high-value resistor to ground) and that's show on the same page.
Assuming you don't already have a power amplifier, again just record the vibrations with your computer to see if they are what you want.
There are audio power amplifier chips if you want to build one. But before you do that, buy one to see how it's going to work and to get an idea of how much power you need. I have [u]this handy little amp[/u] (this particular one doesn't come with a power supply so you have to buy one separately.