There are two different endings.
To get the good ending, take the key from the corpse in Mission 5 that gives you the “Inspect Malchiodi’s Lodging” optional objectives. Follow through with the objective (you’ll need to translate the symbols to get the combination so you can access the information you need), and then, once you reach the Outsider later, talk to Daud and choose the options to release the Outsider instead of killing him.
To get the bad ending, kill the Outsider.
Note: you can do the optional objective and still pursue the bad ending, just not the other way around.
Once you finish the campaign, you’ll unlock Original Game Plus mode, which replaces Billie’s normal powers with the fully upgraded Dark Vision, Blink, and Domino powers from Dishonored 2.