How to Get Numeric Output from Measuring Instruments to Computer?

Does your hygrometer have communicationsport and format that matches one of your computer's communication ports? f so, you should be able to read it, possibly with some programming to scale the value.

I looked up your Testo and you'll have a problem getting data out of it to your PC unless you try something like this. You'll probably kill the thing in the process. I suggest you try going with installed components designed for monitoring. Try www.gesensing.com for starters. Most of their stuff is at least HART capable and most is MODBUS/FIELDBUS designed.

Before you hack into a perfectly good unit, you might want to experiment with building your own that will do what you want. You could then use your current unit as a means to calibrate and verify your home brew unit.

many companies provide the sensors you would need as well as microprocessor

here is the one I first thought of when reading your post: Company Parallax, Sensor Sensirion Temp/Humidity

The circuit and programming would be pretty straight forward, You could use the extra ROM area as data storage to be retrieved when you wanted. But the best part is it is customizable and eXpandable.

I have a favorite saying stolen from a colleague years ago: You can do anything with software, given enough time and money.

Instead of cracking open and soldering stuff together (hardware - ick!), you could actually use a carefully positioned web cam that images the LCD display, then write some software (or find something off the shelf) that will interpret the imagery.

This solution would be speed-limited by the camera quality and its interface and the target's display speed, but you can get very high speed video for a price. It would also be very versatile, as you could point the imager at any display and feed the interpreting software the right data profiles.

(Patent pending, unless someone beat me to it.)