you need only the three pins on one side. The middle one (C) to ground and the outer ones to input A and B. Enable the pull ups on the input pins. Then it should work. To enable the pull up resistor write the follwing code
No, both channels A & B terminals and one of the push button switch terminals will wire to digital input pins that have their internal pull-up resistors enabled. The common on the encoder and other of the push button terminals will wire to ground.
for the button, is it only briefly "HIGH" or is it put "HIGH" when clicked then will only be "LOW" when you click it in again?
When not pressed the button will read as a constant HIGH (due to the pull-up enabled), until you press it and it will then read a constant LOW until you release it.
with the intrnal pull ps enabled, do not use the wring mentioned in your link, instead wire the common pin to ground. If you would go with the wiring you mentioned, the you need on pin A and pinB and the push button an additional resistor to ground (1kOhm approx.)