Update: The Cindered Shadows update is now live, adding the DLC along with a pretty notable patch with quality-of-life changes and bug fixes for all players. To start the DLC, select Side Story from the main menu. Saves and autosaves are separate from the main campaign. It is said to last roughly 8-10 hours. Original story follows.
Fire Emblem: Three Houses will add its Cindered Shadows DLC on Thursday, February 13, bringing a new story about a band of outcast basement-dwellers who consider themselves the unofficial fourth house. The previous announcement trailer didn't make it entirely clear how these new characters would work, but with the big date approaching Nintendo has explained in more detail.
A tweet from Nintendo UK says that progressing through Cindered Shadows will let you recruit the new characters in Part 1 of the main game, then they'll stick around for Part 2. That seems to indicate the Cindered Shadows story will be separate but then hit milestones that add them to the main campaign--but only through the end of the big world-change. After that, you may not be able to recruit them anymore.
The tweet also shows the Ashen Wolves characters interacting in some regular school gameplay scenes, including a nice tea time.
As you progress in Fire Emblem: Three Houses – Cindered Shadows, you can interact with and recruit the four Ashen Wolves in Part 1 of the main game!
— Nintendo UK (@NintendoUK) February 10, 2020
Once they've joined your house, they can take part in battles & classes. They'll also stick with you into Part 2 of the main game. pic.twitter.com/03Q6lkP95v
The four new characters are Balthus, Hapi, Yuri, and Constance, who have dubbed themselves the "Ashen Wolves." The unofficial fourth house has been hiding out in the Abyss, an isolated area in the basement of the monastery. The trailer did seem to indicate this would be a side story rather than an entirely new house selection, since we saw Golden Deer helping discover the Ashen Wolves.
Cindered Shadows is the last piece of the Three Houses Expansion Pass, which costs $25 / €25. The other three parts, which have already been released, included more outfits for Byleth, extra battle maps and support items, and the ability to recruit the Fire Emblem regular Anna.