In this thesis, I describe the design and implementation of the first state-to-state surface scattering experiments for methane from clean single crystalline surfaces in ultrahigh vacuum. The experiments use infrared laser pumping to prepare the incident CH4 in a specific rovibrationally excited quantum state and detect the scattered methane molecules with quantum state resolution using a cryogenic bolometer in combination with infrared laser tagging. To demonstrate the capabilities of this method, I present data on state-to-state scattering of CH4 from a Ni(111) and a graphene covered Ni(111) surface including the rotational and vibrational state distributions of the scattered molecules. For scattering of CH4 in its vibrational ground state, we observe significant rotational excitation. For incident CH4 with 9 kJ/mol of kinetic energy incident at 68° from the surface normal onto a Ni(111) surface at 673 K, rotational levels for J up to 10 are populated for the scattered CH4 corresponding to a rotational temperature of 162 K. The angular distribution of the scattered methane peaks near the specular angle. Both the angular distribution and the large difference between the rotational temperature of scattered CH4 and the temperature of the surface are evidence for a direct scattering process. Incident CH4 is prepared with one quantum of antisymmetric C-H stretch vibration in the v3=1 ,J=3 state by infrared pumping. The rotational and vibrational state distributions of the scattered methane are recorded by the bolometer detector using infrared laser tagging. For scattering from a clean Ni(111) surface, we observe that 40% of the scattered CH4 stays in the v3 state and therefore scatters vibrationally elastically. Vibrational relaxation during the scattering process is observed to populate the v1 state (15%) as well as the 2v2 (2%) vibrational state. No population above the detection limit was found in other vibrationally excited states at or below the energy of the v3 state (~3000 cm^(-1)). 8% of the scattered CH4 was detected in v=0. The fast energy dissipation of 0.37 eV may indicate the participation of electron-hole pair excitation in the scattering of CH4(v3,J=3) from the Ni(111) surface. To investigate the influence of the electronic structure of the surface on the energy transfer during scattering a layer of graphene was grown on the Ni(111) through chemical vapour deposition. The hybridization of the graphene and nickel electronic structures changes the metallic nature of the Ni(111) surface to that of an insulator for Gr/Ni(111). Scattering CH4(v3,J=3) from Gr/Ni(111) results in stronger rotational excitation but weaker vibrational energy transfer. 62% of incident CH4(v3,J=3) remained in the v3 state and no population could be detected in other vibrationally excited states. Relaxation to v=0 was reduced from 8% to 3% for scattering from Gr/Ni(111). State-to-state scattering experiments provide detailed information on the energy transfer processes in surface scattering. The bolometer infrared laser tagging (BILT) technique implemented in this thesis is shown to be a highly sensitive, quantum state resolved detection method that is generally applicable to polyatomic molecules with infared active vibrational modes. In contrast to resonance enhanced multiphoton ionization, BILT does not require a long lived excited electronic state which makes it ideally suited for state resolved scattering experiments of methane.