The electronic band structure is commonly studied by angular resolved photoelectron spectroscopy(ARUPS). ARUPS gives you the joint density of states from the valence bands. By assuming free electron states for the unoccupied states you obtain the density of occupied states. As the momentum of an Electron is connected to its escape angle into vacuum. By assuming dipole selection rules the momentum parallel to the surface is conserved, angular scans of valence states will give the the band structure for k-parallel. For k-perpendicular you have to take valence band spectra in normal emission with varying photon energy, which is most conveniently done at a synchrotron radiation facility. Of course a single crystalline sample is needed and the surface has to be oriented according to high symmetry points e.g. by LEED. For a more detailed study you should read the books of S. Hüfner or H. Lüht, both edited by Springer.
I totally concur Prof. Christian Pettenkofer and Prof. Artur Braun. Where, the band structure is commonly studied by the angular resolved photo-electron spectroscopy.