Refillable mugs can be used at your resort or any other Disney resort for 14 days from the beginning of your stay. They can't be filled at theme parks, water parks, or Disney Springs.
You can purchase a mug (or pick up your mug, if you're on the dining plan) at the quick service food location at any Disney resort. Take the mug to the cash register to be activated.
More information can be found on our Refillable Mug FAQ thread, at the top of this board.