There are many microphone pre-amplifiers available for teh Arduino that are based around common purpose op-amps. An Op-Amp especially suited for audio purposes is the MAX 4466. The Datasheet gives the following application:
In Practice the circuit will look like this. The DC bias for the microphone is taken care of by the resistors R4 and R5. The input capacitor C1 is increased in value to get a better low cut off. The output is rail-to-rail so if the sounds gets loud, the output can go up to Vcc
Vcc is 2.4-5VDC. For the best performance, use the “quietest” supply available (on an Arduino, this would be the 3.3V supply). The output will have a DC bias of Vcc/2 so when its perfectly quiet, the voltage will be a steady Vcc/2 volts (it is DC coupled). If the audio equipment you’re using requires AC coupled audio, place a 100uF capacitor between the output pin and the input of your device. If you’re connecting to an audio amplifier that has differential inputs or includes decoupling capacitors, the 100uF cap is not required.
The gain is depending on R5, P1 and R6. If the current gain is not enough, the value of R6 can be decreased, but in that case the value of C4 needs to be increased in order not to influence the Low pass value.
L1 and L2 are ferrite beads that separate the analogue supply from other supply lines