The best way to cut meat is thinly and against the grain. To cut against the grain, find the way the muscle fibers go and then slice across it instead of parallel to it.
On a piece of meat, the grain is the direction in which the muscle fibers align, and cutting against these results in a more tender piece of meat if cutting a leaner cut, such as hangar steak. By cutting against the grain, the fibers in the meat shorten, making it easier to chew because the fibers are already broken up. Slicing with the grain results in a chewier piece of meat.