Pressure sensors (transducers) typically output a voltage that varies directly with the pressure (or vacuum). It can be as simple as performing an analogRead() on the signal pin of the sensor.
Google comes up with an example at http://david.neonquill.com/projects/rain_barrel/index.html
. In this case he is reading positive pressure; you would be reading negative pressure, but the concept is the same.
For more concrete details you need to contact Jet Fill for the spec sheet on the transducer they sell for the tensiometer.