Go to this website for an online free puzzle:

https://www.mathsisfun.com/games/towerofhanoi.html

Start with 3 disks and learn how to solve it in the minimum of 7 moves.
Then try 4 disks and learn to finish in 15 moves.
Then learn to do 5 in 31 moves.
By going up one more disk at a time you'll make it to 8 in 255 moves.
But if you try to do 8 right away, it gets too confusing.

The key thing to remember for achieving minimum # of moves is this:

Odd number of disks to move - first move is to the target peg.
Even number of disks - first move is to the extra peg.

As you work your way up, you discover the most efficient patterns, as you keep track of intermediate target peg locations.