We present a novel setup for the investigation of ultrafast dynamic processes in a liquid jet using time-resolved photoelectron spectroscopy. A magnetic-bottle type spectrometer with a high collection efficiency allows the very sensitive detection of photoelectrons emitted from a 10 mu m thick liquid jet. This translates into good signal/noise ratio and rapid data acquisition making femtosecond time-resolved experiments feasible. We describe the experimental setup, a detailed spectrometer characterization based on the spectroscopy of nitric oxide in the gas phase, and results from femtosecond time-resolved experiments on sodium iodide solutions. The latter experiments reveal the formation and evolution of the solvated electron and we characterize two distinct spectral components corresponding to initially thermalized and unthermalized solvated electrons. The absence of dark states in photoionization, the direct measurement of electron binding energies, and the ability to resolve dynamic processes on the femtosecond time scale make time-resolved photoelectron spectroscopy from the liquid jet a very promising method for the characterization of photochemical processes in liquids.