A Monte Carlo computer program for following the trajectories of high-energy ions in a lattice has been used to study depth dependence, half-angles, and minimum yields in channeling. The program uses the Thomas-Fermi interaction between ions and lattice atoms and gives the atoms' independent thermal displacements appropriate to the temperature of the lattice. The depth dependence of the nuclear interaction probability near the surface has been calculated and shown to be of importance in understanding other phenomena as well as having an intrinsic interest. Extensive calculations to explore the temperature and energy dependences of half-angles and minimum yields were done, and analytical formulas are given that summarize the computer results. The half-angle formulas give generally improved agreement with experiment and resolve certain discrepancies noted by Picraux, Davies, Eriksson, Johansson, and Mayer between their measurements and earlier theories. Minimum yields were calculated for both single- and double-alignment configurations. The results reveal an energy dependence as well as giving a better description of the temperature dependence and improved agreement with experiment. A relationship is given between the minimum yield and the yield from the surface.