The dynamics of uv/visible laser-induced nonthermal desorption of neutral molecules from metal surfaces are studied by Liouville-von Neumann equations for quantum open systems. A one-dimensional, two-state Gadzuk-Antoniewicz model is adopted, representative for NO/Pt(111). Electronic quenching due to coupling of the adsorbate negative ion resonance to the metal electrons is treated within the Lindblad dynamical semigroup approach. Both indirect (hot-electron mediated) and hypothetical direct (dipole) excitation processes are considered. For the indirect pathways, DIET (single-excitation) and DIMET (multiple-excitation) limits are studied using one- and double-dissipative channel models, respectively. To reproduce experimental desorption yields and desorbate translational energies, we estimate the quenching lifetime for NO/Pt(111) to be less than 5 fs. We also extend previous quantum treatments of photodesorption processes to the case of coordinate-dependent quenching rates. Further, the characteristic scaling laws of desorption yields versus laser fluence are derived for each of the individual excitation pathways. Finally, the possibility to control photoreactivity at surfaces by different, vibration-promoted schemes (surface heating, ir+uv two-photon strategies, use of pulsed uv lasers) is examined.