You can check the A/D converter and your software with a pot. There is some information
here.
Testing you mic & preamp circuit is a little trickier. It's probably best to get a pre-built breakout board for testing purposes. When you get everything working with the breakout board, you can try your own mic & preamp circuit if you want.
If you have a multimeter (which you probably should have) you can measure the DC output bias as well as the AC signal. (You may not be able to measure the un-amplified AC signal from the mic, because it's only a few millivolts.) You could also test your mic/preamp by plugging it into your stereo system or line-in on your computer's sound card... But, I really don't recommend it because there is a small chance of damaging your stereo or soundcard if there's something wrong with the circuit.
I tried that, but all I got from trying any of those results was a random number repeated that did not change
What does that mean? If it's repeated and doesn't change, I wouldn't call that "random".
When you read/sample audio the numbers normally "look" random because you are reading "random" places along the waveform. The breakout board normally has it's output biased 2.5V. With silence, you should get readings around 512. As the sounds get louder, the numbers should "spread out" and you should get
some bigger numbers
and some smaller numbers with lots of "random" values in-between. The
average should remain around 512.
This isn't necessary if you just want to get the "loudness", but with "normal" digital audio the waveform is sampled at a constant-known rate (44,100 times per second for a CD). The values look random, 'till you plot them at the same constant-rate. Then you can "connect the dots" and re-create the waveform. And in fact, real-world sound/audio is quite "random". If you've ever seen a VU meter, the readings would look random if you are not listening to the sound.