The first step would be to think about whether what you are measuring is ohmic--does it obey Ohm's Law? And at what test voltages?
Then it is a matter of supplying the test voltage and measuring the current with a picoammeter or electrometer. You'll likely need an enclosed chamber to eliminate air currents and so forth. I can't say I have experience with 10^15 ohms, the biggest resistor I have is 10T, or 10^13 ohms, and for that using 100 volts and a picoammeter, well it's not easy, especially if you don't turn the ceiling fan off. It sort of worked for me. What are you measuring?