The curve is the spectrum of the X-rays emitted by an X-ray tube with a rhodium target(bremsstrahlung). I don't know how do experimenters get it. Do they first measure the waveform of the radiation then perform Fourier transformation?
Energy spectra like that are commonly obtained using energy sensitive photon counting detectors (such as cooled high purity germanium detectors). Detected photons are categorized by the amount of energy deposited within the detector. Collect enough of them and you get an energy spectrum.