My friend wants help setting up a system to record city hall meetings.

About 8-10 speakers. The current setup is a single smartphone in the middle of the room. At the best of times, it's barely intelligible. They now have plexiglass barriers between them, plus they wear masks.

I'm about as far away from an audiophile as exists, so talk to me like I'm a complete idiot.

How does one record audio from multiple sources and manage those sources when two people are talking at the same time?

Disclaimer:  I'm not an expert.

First things first, what is your budget?  Can you justify spending enough money to put a microphone in front of each speaker?

You need microphones, microphone cables and a mixer with cables that feed the recording system.

The amount of microphones depends on how many different sources you need to record. In this case, 8-10 microphones.

Mixers come with 2, 4, 6, 8, 12, 16, 24 channel inputs for each microphone and they get more expensive as the amount of channels increase.

The kind of mixer you will need to get will depend on how many microphones you are using. Most likely you will need a 12 channel mixer.

You adjust the microphone input levels so they aren't too low or too loud.

You then feed the output from the mixer into a recorder that could be a PC with an audio recording application or a dedicated digital or analog recorder like a reel to reel tape or cassette deck.

You can listen live by using headphones plugged into the mixer and you can also listen to the recording by feeding the recorder output back to the mixer. This way you can hear how it all sounds and make adjustments.

The finished product is the saved as a digital audio file on a PC or an old school analog recording such as a reel to reel tape or cassette deck.

That's the basic overview of audio recording with microphones.

It is doable for a novice, but it will be a somewhat steep learning curve.

If you feel its too much to do, then I suggest you hire an audio engineer to record all that, but be prepared to pay big bucks.

Either way, someone will have to shell out cash as well as time spent learning how to run it all and then recording it.

Shure SM57s are about $100. You can get a nice USB mixer with separate outputs for <$500. This is critical imho. The USB part means it shows up as an audio interface in your Digital Audio Workstation (DAW). I'm a big fan of Reaper and it's only $60 but extremely powerful. A lot of USB mixers, though, mix the signal and output all channels to one or two outputs. Optimally you'd want each channel to appear individually in the DAW so you can record each mic as an independent track. Apply some vocal-specific FX to normalize, boost, etc and you should be able to get some good recordings.