After you've installed this DLC you can load a saved game and you'll be informed about the possibility of starting a new quest. Important! You won't be allowed to move on with this mission until you've left [Lothering] and therefore completed Lothering and the imperial highway main quest! I would recommend starting it as soon as possible and to install The Stone Prisoner along with the game, so that during its course you'll have a chance to begin collecting new types of crystal for your future companion (golem).
An important thing about The stone prisoner is that the difficulty level of this DLC will change depending on your current progress and an ideal moment to start the first mission would be prior to completing main Plague quest in Orzammar - Paragon of her kind. Otherwise you may encounter some problems activating golem's personal quest not long after the creature has joined your team. Don't forget to free some space in your inventory, because you'll have a chance to collect a lot of useful things in the near future, especially when it comes to finding crystals. A party chest provided by Warden's Keep DLC may come in handy here.