After downloading and unzipping the DLC, right-click the CrossCode Application, and click "Show Package Contents." Then, go to Contents -> Resources -> app.nw -> assets -> extension. Then, drag the unzipped DLC folder into this location. Then, launch the game. On the Main Menu, if you check the installed DLC list, it should now include "Post-Game" (or something along those lines).
(Very Minor Spoilers Below)
To actually begin the DLC, (Assuming that you've already beaten the game, gotten the "Good Ending" and are currently at the point just after the post-credits scenes are complete), walk to the right. If you didn't get the "Good Ending," walk left, and either figure out how to get it, or google it shouldn't take more than 10-15 minutes, tops, to get the "Good Ending," once you figure out what to do.