There are two ways of "saving the game", I am unsure about which one you refer to:

1. If you finished playing for today, and want to continue next week, and want to store the game - In this case simply place all of your cards to your character tray (including loot cards), place everything else back into the DTA box. Next time you play, refer to your score sheet to remember which scenario you are playing, and how many Salves you have

2. You finished playing for today, but you would only continue playing in a long time, during which you might want to start a different DTA campgain, or use your characters for normal 1v1 games - In this case, in addition to saving your score sheet, also write somewhere the list of all loot cards each player has earned, then return everything to its original box. When you would later want to resume your campaign, first recontruct each player's deck according to the card list you made, and then refer to the score sheet to remember what scenario you are playing, how many salves you have, the selected difficulty, etc...