The Tower of Hanoi

This clip is a home video of a man solving a 6-ring Tower of Hanoi problem at the Haifa Science Museum. (Many other videos of how to solve this problem with up to 10 rings can be found on YouTube.)

How could someone solve the tower of Hanoi problem strategically? Judging from what you have seen in the video clip, how would you explain the process to a friend who is unfamiliar with the Tower of Hanoi?