You can push boulders by standing next to them and pressing the A button. However, there are some conditions:
* You need the Strength HM: This is a crucial requirement. Strength is a move you learn from the gym leader in Pewter City.
* The boulder needs to be a certain size: The boulders you can push are usually small and round. Larger boulders cannot be pushed.
So, to summarize, you don't need to learn a special move to push boulders, but you do need to have learned the Strength HM first!