I recently inherited the leadership of the audio/video committee at my church. I bought a cable tester to check all the audio cables and adapters, and tossed anything that didn't pass. Now I'm faced with a small collection of microphones (approximately ten) that nobody seems to know which of them are good and which are defective. This past Friday one of my guys was doing a live event and ended up selecting a microphone that is apparently bad. How do I go about testing these microphones to make sure they're working properly as designed?
If you mean bad in the sense in which a bad cable is bad – i.e., broken or fine – simply connect the microphone to a mixer with headphone output or an active speaker, tap on the microphone and say something into it. You'll notice if one doesn't work, there will be no sound! Or e.g. heavily distorted sound, or failing sound when you jiggle the plug etc.
Determining how good a microphone is is another matter. Reasonably robust dynamic microphones tend to remain quite constant in their sound quality up to the point where they completely fail, so if you see a microphone of a good brand that does work at all you can usually assume that it works well, for instance having some SM58s is always a comfort. Though different types of microphones do of course perform different for different tasks: reliable as such dynamic microphones are, I'd hesitate to use them to e.g. record a piano or other acoustic instruments because the sound isn't quite as "open" as it ought to be. Usually, one has to know how each microphone sounds, but that requires a lot of experience. It is also possible to precisely measure all the acoustic properties of a microphone, but that's really complicated and doesn't seem to be what you need.
I'm afraid this might sound cliche or condescending, but try them out and trust your ears. If you knew what each mic was you could look up all their specs, but that information may not be all that useful to you. I could, and would be happy to answer questions about what those specs mean, but I think it's much more useful to you to just trust that the one that sounds the best is likely the best.
You should also google the makes and models of each of the different makes and models to find out what they are best used for (voice, instrument, etc.) or ask about them on hear. In the end I'm guessing you took on this responsibility less to learn about which microphone is best for what and more to help out your church. That's why my advise to you is to ask for the opinion of others (on here or IRL) and trust your ears. Learning the specs, and what the specs mean is one thing, but learning what the changes in these specs sound like, that's a totally different thing. To quote (or at least paraphrase) Joe Meek "If it sounds good, it is good."