Good carving is neither an art nor a science, but an acquired skill.
A knife is essentially a very finely toothed saw and it should be used in the same way, that is, drawn back and forth through the meat it is cutting. Never try to push even a sharp knife through meat without this sawing action. If the knife is sharp, the backward and forward motions can be long and light. In this way less-jagged slices are removed. Try to keep the knife at the same angle all the way through the joint and try to take a slice of equal thickness. This is not always possible, as with the first cut from a roast joint of beef.