The original article is published in Nature, doi:10.1038/nature08967. I just read it (or, gave it a 60%-level skim). The paper is very detailed, if terse, and the experimental approach is complex, if clever, so I’ll give only a short summary.
The “drum” is piezoelectric, so it can be coupled to a circuit capacitively for readout and manipulation. That readout and manipulation is, in turn, provided by a qubit, which is a small two-state quantum system. The energy gap between the ground state and excited state of the qubit can be tuned inductively (i.e., magnetically).
The main “trick” of the experiment is that you can tune the qubit’s energy gap to be either close to or far from the lowest frequency mode of the drum (energy E=hf). When these match, they exhibit the usual coupled resonator phenomenon of sharing energy back and forth. (Think: classical weakly coupled pendula. The “trading” of energy here, though, is between two systems that have only two accessible states each.)
The first half of the paper describes multiple methods used to demonstrate that they can get the coupled system into its ground state. The actual, physical, measurement performed at any given instance is What state is the qubit in? This is a quantum mechanical question, so they repeat this “~1000” times when they ask it so that they can actually determine P(e)=What is the probability that the qubit is in the excited state?
That’s the crux of it. They proceed to plot P(e) under various configurations of: (1) the quality of “tune” between the qubit and the mechanical resonators, (2) how long they hold the pair in tune, (3) how long they keep them out of tune (to let the drum’s state evolve a bit before reading it out resonantly), (4) how long and hard they ping the drum through a separate excitation channel (a blast of microwaves).
They look at P(e) as a function of all these things, and they extract quantities such as the energy transfer time, the resonator relaxation time, etc. These data are in excellent agreement with the quantum mechanical expectations, demonstrating, among other things, that the drum and qubit indeed seem to become quantum mechanically entangled and seem to have quantum mechanically “uncertain” states.