To install the Coop Campaign mod, navigate to the Mods / Browse Mods page in-game.
Then, either search for "coop campaign", or sort mods with the Campaign tag by most downloads to find the mod:

With the Coop Campaign mod selected, click the Install button.

To host one of the coop campaign levels, open the Multiplayer menu in-game, then click the Host button.

When prompted, set the Game Mode to Custom Scenario and choose the desired level (all levels will begin with "coop-campaign\"). Then click the Host button.

Once in the lobby, invite your friend, select a difficulty, and ready up. No other settings need to be changed.