Capacitive sensor

Is there any way to measure capacitance of an object? Lets say paper, plastics..etc.

No need. It's zero.

Or are you trying to measure the dielectric constant? That's quite straightforward. Place the object in between two parallel plates making sure there is no air or anything else in between the object and the plates, measure the capacitance, then compare it with the capacitance of the same plates placed near each other in vacuum. As distance between the plates is very important, make sure you know the exact distance (as in, at least three significant digits) for both setups, preferably keeping the distance equal for best comparison. Bigger plates are better, as you have less edge so less edge effect disturbing your measurement.

What happens if there's space between the plates and the material?

The extra space reduces the capacitance.

For a parallel plate capacitor, C is proportional to A/d, where A is the area of the plates and d is the spacing between them.