Arduino reading double-din radio volume rotary dial knob
Your last photo shows that two of the device's pins are grounded to the large PCB "pour". That leaves three pins for the switches - two encoder pins and one push-to-make.

The wiring will usually be as shown in Figure 1.







simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. Encoder and switch wiring.

The encoder outputs will be as shown in Figure 2.



Figure 2. Encoder count-up / count-down sequence.

Rather than spend too much time messing with the PCB I would be inclined to de-solder the resistors, cut the traces between them and the switch terminals and then solder flying leads from the switch terminals to your microcontroller. If you use internal pull-ups on the micro then you can omit R1, 2 and 3 of my Figure 1.



From the comments:


  Since this is an infinite turn in either direction how would i determine, say for music volume, if its back at 0 or if its all the way up? 


You can't. There is no zero position and most of these devices are low resolution encoders with as few as twelve steps per revolution. In use it takes several revolutions to go from zero to maximum. They're quite common on car radios so you should play with one for a while to get the feel of the system you are emulating.

On power-up you have to assume an initial value. This could be zero (muted) or some audible but safe value that isn't going to wake the baby. After that you keep track of the adjustment in code and stop the counter at zero when turning anti-clockwise and maximum when turning clockwise. Obviously the user can keep on turning but your code will reject additional counts until the direction is reversed.