how many buttons will they allow me to have
It will be 8 per chip so for four chips that gives you 32 inputs.
This will "cost you" some inputs / outputs on the arduino.
One way to wire it up is to have the three select lines for all 4 chips wired in parallel and then the common from the chip to one of 4 separate arduino inputs.
You can wire it up like in this project:-
http://www.thebox.myzen.co.uk/Hardware/MIDI_Footsteps.html
That shows just two chips and uses the analogue inputs. If you have just push buttons you can use digital inputs instead of the analogue ones.