State-to-state molecule/surface scattering experiments prepare the incident molecules in a specific quantum state and measure the quantum state distribution of the scattered molecules. The comparison of state resolved experiments with theory can serve as stringent tests of the molecule/surface interaction potential and of the scattering dynamics. The overall motivation is to develop a predictive understanding of the molecule/surface interactions and reactions needed for the understanding and optimization of heterogeneous catalysis. In this thesis, I describe the design characterization, and first applications of a new apparatus, dedicated to performing state-to-state surfaces scattering using the bolometric infrared laser tagging detection (BILT). An important advantage of the BILT detection method over other state-resolved detection techniques such as resonant multi-photon ionization (REMPI), is its applicability to any molecule with an infrared active vibrational mode and a rotationally resolved vibrational gas phase spectrum. For example, BILT detection can be used to detect important molecules such as methane and carbon dioxide for which REMPI detection is not possible. Our new state-to-state scattering machine features a liquid helium-cooled bolometer detector installed on a rotatable lid allowing independent variation of the incident and the scattering angle. With this capability, one can study energy transfer such as the conversion of translational to rotational or vibrational energy as well as vibrational energy redistribution for molecules colliding with a well-defined single crystal surface at a wide variety of scattering geometry. To demonstrate the capabilities of the BILT machine, I studied the rotationally inelastic scattering of CH4 from Ni(111). The results show that rotational excitation depends not only on the kinetic energy along the surface normal but also on the parallel component although with lower efficiency. The extent of rotational excitation is found to increase with increasing surface temperature. The conversion efficiency appears to be higher for low velocity component normal to the surface. The observations indicate a mechanism of rotational excitation by phonon annihilation with the probability related to the relative velocity of the incoming molecules and surface atoms. Using the experimentally determined formula which takes into account the conversion efficiency of the normal, the parallel component of incident kinetic energy, and the surface thermal energy to the rotational energy, the mechanism of rotational excitation of CH4 scattering from Ni(111) is quantitatively unraveled. Besides rotational inelastic scattering, I report very distinct behavior of vibrationally inelastic scattering of CH4 from clean Ni(111) and Gr-Ni(111). Vibrational energy transfer to the surface dramatically changes when a clean Ni(111) surface is covered with a single layer of graphene. Theoretical calculations based upon reaction path Hamiltonian suggest that the probability of the vibrational energy transfer is related to the catalytic activity of the surface impact sites. Therefore, by monitoring the fate of the initially prepared vibrational energy, the state-to-state surface scattering technique can potentially serve as a probe of the catalytic activity of surfaces.