A high peak brilliance, laser-based Compton-scattering γ-ray source, capable of producing quasimonoenergetic photons with energies ranging from 0.1 to 0.9 MeV has been recently developed and used to perform nuclear resonance fluorescence (NRF) experiments. Techniques for characterization of γ-ray beam parameters are presented. The key source parameters are the size (0.01  mm^{2}), horizontal and vertical divergence (6×10  mrad^{2}), duration (16 ps), and spectrum and intensity (10^{5}  photons/shot). These parameters are summarized by the peak brilliance, 1.5×10^{15}  photons/mm^{2}/mrad^{2}/s/0.1% bandwidth, measured at 478 keV. Additional measurements of the flux as a function of the timing difference between the drive laser pulse and the relativistic photoelectron bunch, γ-ray beam profile, and background evaluations are presented. These results are systematically compared to theoretical models and computer simulations. NRF measurements performed on ^{7}Li in LiH demonstrate the potential of Compton-scattering photon sources to accurately detect isotopes in situ.