A circuit that is net charged What differences would you measure if a circuit were significantly charged negatively? Would the resistance change? To be clear, I mean that excess electrons are added to the system. The circuit can be of any kind you can imagine. 
 A: There are broadly three classes of materials: conductor, semiconductor, insulator.
The conductor contains a LOT of electrons per unit volume. If you were to charge it, you would add a few more electrons. How many?
Let's take copper. It has roughly $8.5\cdot 10^{28}$ electrons per $m^3$. If you have a wire of radius $r$ the number of electrons scales with $r^2$ and capacitance scales with $\log{r}$. So the thinner the wire, the more important the effect of surface charge on total number of electrons. 
I will leave it up to you to calculate how thin a wire would have to be before surface electrons contribute significantly to the measured resistance. A quick "back of the iPhone" estimate: For a macroscopic wire capacitance might be a few 100 pF per meter so you could get about $10^9$ electrons per meter on the surface. That would be roughly the same number of electrons as we can get in a 1 nm diameter wire (assuming that at that curvature a wire can hold 1 Volt without discharge to the air - which seems unlikely...) Good luck measuring that.
For semiconductors and insulators the number of charge carriers is smaller. This will make the math slightly more favorable. But note that surface effects (would surface electrons even contribute to conduction?) would be very important to consider - the number of electrons in an insulator does not tell the whole story (there are plenty of electrons but they are not free to move. Not at all obvious it would be different for surface charge).
A: To do this experiment, you will need:
1> a grounded, sheilded cable, (to prevent magnetic interference)
2> an ability to apply a voltage from the cable to ground, (say a battery, or better a variable DC source, with the postive terminal grounded and the negative one attached to the cable) and
3> a sensitive ohm-meter.  
Then compare the ohms through the cable with voltage applied or not to the cable, to generate more electrons. Keep a log of your results.  It might be wise to compare various materials for the cable, to see if some materials have more "hole effect" than others. I would also advise not going above two car batteries in voltage unless you are a trained electrician.  (24 volts)
