Haven't read the paper but I've been to a seminar from one of the paper's authors.
The bar is a harmonic oscillator---you don't have frequency control of such an oscillator, because (just like a clock pendulum) no matter what the amplitude of the oscillation is, the frequency is the same. The ground state and the |1|> state and the |2> state all have the same frequency. For that reason, quantum control is especially challenging.
Classically speaking, you would imagine that if you give a pendulum a very strong kick you'd put it into the state with energy E, and if you kick it half as strongly it'd get into a state with E/2, and so on. You might imagine that if you gave it a kick of energy hbar omega, you'd get the oscillator into the state with this energy. In a quantum system, though, it turns out that this technique produces a "mixed state" of uncertain energy.
Cleland et. al. were able to construct a coupled circuit with two quantum systems in it: system #1 is the mechanical state of the bar, system #2 is the number of microwave photons in a waveguide. Cleland et. al. were able to put a single photon into the waveguide, a technique I believe his lab developed; this photon can be manipulated and detected using some Josephson junction mumble mumble that I don't understand. The key to this experiment is cross-coupling between the waveguide and the resonator. This allows the single photon you injected into the waveguide to turn into a phonon in the resonator, and then you know that you're in the one-phonon state. Then the phonon leaks back into the waveguide mode (as a photon) where you have a chance to measure it. By putting complex photon states into the microwave system, the experimenters can cause any desired state to shuffle its way over to the resonator. You can do a sequence of time-domain measurements on the microwaves---you can see how long it takes the photons to go away, then you can see them come back after hanging out on the resonator for a while, and you can see five or six repeats of this sloshing before the system damps itself out. The detailed properties of this time-evolution (which I can't claim to understand terribly well) ultimately tell you that the resonator portion of the system was indeed behaving quantum-mechanically.
The resonator itself is neat---it's a little suspended film with some sort of piezoelectric property which means that it has a mechanical-to-electrical coupling. What's neat about it? You may already own one---they're part of the high-frequency RF filter in the front end of your cell phone.