How do I connect 3 audio inputs with a switch?
You need something like that but if you have stereo signals you need a 2 pole three way switch.

There will be two common pins you put one to the left input of the amplifier and one to the right input.

It will be similar to the schematic below (I could only find a 2 pole double throw switch but it will be similar for a 3 way but with more inputs).

The grounds for all the inputs and outputs are all connected together.

For the switch you may find a rotary switch is more easily available and easier to mount as it only needs a round hole in a panel.

For example:
Two pole 3 way switch 






simulate this circuit &ndash; Schematic created using CircuitLab