How do I obtain readings using an AD8302?
Those power and phase detectors are still analog outputs - they output a voltage to represent the power level on the input. You still need to use some for of digitizer, be it in a prebuilt piece of equipment such as a multimeter or such, or a ADC board you design yourself. You can't just plug the powerdetector into your computer and expect results to come out.

The datasheet shows that you should expect aproximatly 30 mV/dB slope. 

The advantage of using prebuilt hardware is that the drivers for matlab and labview potentially already exist. You could also look at ADC devboards, which sometimes come with software to interface to matlab and so on.