If, according to the weather forecast, the current humidity is 90%, how can I calculate the volume of water that could be extracted from a certain volume of that air?
You need a psychrometric chart.
On the x-axis, input the value of a common air thermometer (it's the dry bulb temperature). Now follow a vertical line until you reach the red curve that reads 90% relative humidity.
Follow the horizontal line to the y-axis on the right and that humidity ratio will be the ratio of water versus dry air (mass-wise). That is, 0.015 means that 1.015 kg of your current air has 1.000 kg of dry air plus 0.015 kg of water vapor.
To turn that into volume of water per volume of air (air is different from dry air), you'll have to do a little math and unit conversion. You can use 1.2 kg/m³ as the density of dry air (at 20°C) if it helps.