The topic is covered here, however the recursive approach can be confusing if one is not familiar with the concept. The algorithm works by first recursively moving all but the last disc (a smaller problem instance) via the cache peg away, then "actually" moving the last disk to the destination peg and then moving the tower to the initial peg. In effect, relying on the recursion, the disk at the bottom is moved to the destination peg, which is impossible to do directly as is is no valid move. In the recursive call, the three pegs change the roles such that always an empty peg becomes the cache. This is understood best if you imagine the pegs not to be arranged in the line but in a circle. Unlike other problems, here the recursive call comes first and then the "actual" movement is done.
The question can be seen as a duplicate of this question.
