Transitions from bound atomic Rydberg Stark states in a static electric field to autoionizing Rydberg states above the electric-field-induced ionization threshold are studied using a broadband, tunable free-electron laser (photon energy 160-1400 cm(-1), pulse duration similar to 1 ps) and compared with multichannel quantum defect theory calculations. An atomic streak camera is used to record the time-resolved electron emission transients of the autoionizing atoms. For Stark states located on the downfield side of the potential, the far-infrared ionization spectrum is found to be smooth and the electron emission prompt (<2 ps), whereas for Stark states located on the upfield side, the far-infrared spectrum has sharp resonances, and the lifetime of the quasicontinuum states is considerably longer. The electron-emission transients from optical ionization of ground-state atoms are compared to transients from far-infrared ionization of Rydberg atoms, showing that the angular motion of the wave packet is responsible for the ionization dynamics for both cases, but different coherent superpositions of angular momentum states are excited depending on the initial state. Finally, we discuss the feasability of using Rydberg atoms as an ultrafast far-infrared detector, starting from a downfield state, or as a wavelength-selective detector, starting from an upheld state.