I'm getting a noisey/square wave output for my mux/demux?
Vee should be connected to Ground, or to a negative supply.

As this is a CMOS part, all digital inputs MUST be connected (possibly via a resistor) to either Vcc or Ground at all times - otherwise the inputs may float to a "maybe" state, with unknown consequences.

Connect all S0 - S2 and /E to ground with 10K (or so) resistors.  Also connect A0 to ground with a 10K resistor, and A1 to Vcc.

Now, the output should initially be Low.  Pulling S0 up to Vcc will select A1, and the output should be High.