Electrical – How to read out data from this moisture sensor

It's called capacitive because the two copper planes in your sensor are the two plates of a capacitor. In a physics textbook these two plates might be drawn facing one another, with empty space in between. Put a material between the plates, and the capacitance, which is a measure of how much charge is on the plates for a given voltage, changes. This material is called the dielectric, and how much the capacitance changes for a given material is called the dielectric constant of the material.

Dry soil has a different dielectric constant than wet soil, which means that a sensor in wet soil is going to have a different capacitance than one in dry soil.

How do we measure this capacitance? One way is to use an RC circuit, and to measure the voltage on the positive terminal of the capacitor. This terminal is going to reach 63.2% of its maximum voltage \$RC\$ seconds after a voltage is applied, where \$R\$ is the resistance and \$C\$ is the capacitance. By turning on the supply voltage at a time \$t_{on}\$, checking the voltage on the positive terminal of the capacitor continuously until it exceeds 63.2% of the supply voltage, and recording the first time where that voltage was exceeded \$t_{c}\$, we can calculate the capacitance (we know the resistor value because we chose it).

That is,

C = \$(t_{on}-t_c)/R\$

This tutorial will show you how to set something like this up on an Arduino. https://www.arduino.cc/en/Tutorial/CapacitanceMeter

I'll resist baring anything with you, but inexpensive RH sensors are usually capacitive- using a hygroscopic (moisture absorbing) polymer. Water is a polar molecule and causes a large increase in the dielectric constant of the polymer. This same method can be used to measure moisture in a bulk material that absorbs water.

Yes, you have to use AC to measure capacitance. There are simple circuits that can be used for this, or, as this is 2016, you could leave the hard work to IC engineers and buy a capacitance-to-digital converter chip. They will typically work up to maybe 5-10pF full scale range (changing capacitance) so the measurement cell can't be too large. Analog Devices makes some that are not EOL.