According to the press release from the Argonne National Laboratory, the process occurs using an acoustic levitator. The two small speakers generate sound that is barely audible to the human ear. One wavelength is emitted from the top speaker and the other from the bottom so they perfectly interfere with each other. This triggers a phenomenon known as a standing wave.
The acoustic pressure from the standing waves cancels out the effect of gravity at certain points, called nodes, which allows light objects to be levitated.