This post is a mini-summary of a Perspectives piece I wrote for ACS Nano. One conceptually simple way to measure the electronic properties of materials at the atomic scale is to use a "break junction". Imagine taking a metal needle touching a metal surface, and slowly lifting up on the needle. At some point, the needle will come out of contact with the surface. As it does so, at the last instant, the contact between the two will take place only at the atomic scale. If you hook up one end of a battery to the needle and the other through an ammeter to the metal surface to measure the flow of current, you can measure the electrical conduction throughout this process. Thanks to the availability of high speed electronics these days, it is possible to record conductance, G, vs. time data throughout the process. A standard analytic approach is then to compile a histogram of all the data points, counting how many times each value of G is measured. As explained here, the most stable junction configurations naturally have more data points, and this will lead to peaks in the conductance histogram at the values of conductance corresponding to those configurations. Molecules may be incorporated into such junctions (as I've written about here). Since it's possible to set up a system to make and break junctions repeatedly and rapidly in an automated way, this approach has proven very fruitful and revealing.
Of course, only looking at the histograms is wasteful. You actually have an enormous amount of additional information contained in the G vs. t traces. For instance, you can check to see if the occurrence of a "plateau" in G vs. t at one conductance level always (or never!) correlates with a similar plateau at a different conductance value. These kinds of cross-correlations are best represented in two-dimensional histograms of various types. Makk et al. have written a very clear and tutorial paper about how this works in practice, and what kinds of things one can learn from such analyses. It's definitely worth a read if you work on this stuff, and it's also a great lesson in how as much of your data as possible.