What is the proper and up to date method for multiplexing digital inputs?
To do "multiplexing" you'd need some way to control the select line of the mux (which means an extra log base 2 inputs according to the number of sensors you have, so for 16 sensors you'd need four more outputs to control the select line).  And you'd need a bunch of AND gates to select which mux channel you want to connect to the inputs.

If they had CS (Chip Select) pins themselves, you could avoid the gates.  But you still have to worry about converting 4 outputs into 16 chip selects; could probably get a 4-bit decoder to do that.

I don't like any of those solutions, though.  They're very messy.  Personally, I would use a couple I2C input buffers and then wire all the inputs to those and then read the buffers with the Arduino.  Easier to handle, and only uses two inputs on the Arduino.  Easily extensible too, so long as you don't have any address conflicts.