We have developed a material specific theoretical framework for modeling scanning tunneling spectroscopy (STS) of high-temperature superconducting materials in the normal as well as the superconducting state. Results for Bi2Sr2CaCu2O8+delta (Bi2212) show clearly that the tunneling process strongly modifies the STS spectrum from the local density of states of the dx2-y2 orbital of Cu. The dominant tunneling channel to the surface Bi involves the dx2-y2 orbitals of the four neighboring Cu atoms. In accord with experimental observations, the computed spectrum displays a remarkable asymmetry between the processes of electron injection and extraction, which arises from contributions of Cu dz2 and other orbitals to the tunneling current.