We describe an experimental system designed for single-shot photoelectron spectroscopy on free atoms and molecules at the Free Electron Laser in Hamburg (FLASH at DESY). The combination of the extreme ultra-violet (EUV) Free Electron Laser and a temporally synchronized optical fs laser (Ti:Sapphire) enables a variety of two-color pump-probe experiments. The spectral, temporal and spatial characteristics of both the EUV FEL and the optical laser pulses, the experimental procedure to control their overlap as well as the performance of an electron spectrometer used to obtain single-shot photoelectron spectra are discussed. As an illustration of the capabilities of this set-up, some results on two-photon two-color ionization of rare gases are presented.