The coach will usually clip a small microphone on the collar of the clothes.
The signal from the microphone, in turn, travels through a signal wire to a transmitter that's going to be hanging on it.
The transmitter sends the signal to the back of the stage.
There are wireless receivers at the back of the stage.
After receiving the signal, it is sent to the amplifier.
The amplifiers push the speakers.
So, I have to ask you, what do you need this for?
Because a small collar microphone, a transmitter that hangs from your waist, and a wireless receiver for the back of the stage - are sold as a set. Not cheap.