Hello and welcome to the fascinating and (sometimes crazy) world of audio. Whether you are looking to record your ensembles or amplify them for a greater audience, it is hard to figure out where to start.
For the sake of simplicity, the majority of this guide is broken down into two sections "Recording" and "Amplification". Most often you will find that many of the techniques and suggestions are shared between the two. The two categories can be defined as:
Recording is the process capturing your ensemble's/musician's sound through some sort of "Microphone" and recorded to some form of medium such as a DAW (Digital Audio Workstation), external device like an audio recorder or digital device (phone, tablet, etc.). There are numerous reasons to record including: concert recordings, auditions, playing tests the list goes on and on.
Amplification is the process of capturing your ensemble's/musician's sound through some sort of Microphone, amplifying it and playing it over some sort of PA System (Public Address) in order to make them sound louder.
Signal flow in the most plain terms is the direction signal (source/original sound) travels on its way to being recorded or amplified. This is usually depicted through diagrams which show how microphones are connected and then routed to their destination.
For both applications, you will need a microphone, connected to a Mixer/DAW connected through a microphone cable (usually XLR).
For amplification, the microphone(s) are connected with XLR cables to the mixer. Once the microphone is connected to the mixer, they are plugged into the built in amplifiers which then allow the mixer to modify and/or adjust the signal before sending it to the the PA (speakers).
Depending on whether you have active or passive speakers, you may need an amplifier to amplify the sound before it reaches the speakers.
For recording, the microphone(s) are connected with XLR cable to some form of Audio Interface. The audio interface contains an A/D (Analogue to Digital) converter which takes the signal and converts to a digital signal. This signal is then sent to the DAW where it is then recorded.