Does anyone know how to program a repetative motion robot (see description)? Answered

This is mostly out of a theory and curiosity, but if I were to make a robotic arm and I wanted to make it do repetativve motions, how would I make It recognize/remember the movments and how would I make it perform them. It would be a direct teaching unit (meaning I would move the robot and it would remember the movments) so how would I make it run or hook it up to a computer and how would I program it with the direct teaching. If this impossible or extremeny difficult, please recommend a different technique. Please give me good, detailed instructions.