Honor Thy Mother
If this is your first visit back to Applewatch since you completed the "Next of Kin" mission, you'll find five graves lined up outside the house with epitaphs for you to read. Activating Perennia's tombstone will generate a ghost that will start hurling frost-based spells at you (no biggie if you're a Nord). The rest of the tombstones are just for reading. If you fast-travelled and have Shadowmere with you, he will almost certainly take care of the Ghost himself. Otherwise, take care of it and collect your Ectoplasm. There is a Fine Steel Longsword on Caelia's grave, which you're welcome to take (if you're completing this quest at very low level, it might be better than what you're finding in stores or as loot).
When you enter Applewatch, you'll immediatley know that you're too late. The Black Hand has found Lucien Lachance. His corpse is strung up by its heels in the center of the room - activating it will get you a journal entry to the effect that he's dead (no duh!). You'll find the four remaining members of the Black Hand (Arquen, Mathieu Bellamont, Banus Alor and Belisarius Arius) in the room as well. Arquen tells you that they have killed the traitor and have decided to promote you to Speaker. Unfortunately, because the Listener and his successor are dead, they will need to consult the Night Mother for direction on what to do next. They do not hold you responsible for their deaths; you were only following the orders of your Speaker, after all. You need to talk to Arquen between midnight and 3 a.m. and let her know that you are ready to begin the ritual.
If you did not bring the head from the cellar, you should follow those instructions because there isn't anything else for you to do here. There is no time limit on talking to Arquen, so if you'd like to go take care of other business, feel free. Just make sure that you talk to her between midnight and 3 a.m. If you talk to her at any other time, she'll just tell you to come back during that time.
If you did bring the head from the cellar, you can drop it anywhere and talk to the other three Black Hand members (it should be pretty obvious that Arquen is not the traitor since she was the next target). Mathieu Bellamont is the only one who even notices it. Most suspicious. Once that's out of the way, you can go talk to Arquen at the appropriate time.
When you tell Arquen that you're ready, all five of you will appear around the statue of the Lucky Old Lady in Bravil. Arquen will brief you and begin the ritual, the statue will change and move back to reveal a trapdoor, and the other members of the Black Hand will enter. If you feel like you need it, activate the statue for your Luck blessing. It's the last time you'll be able to get it because the statue will have a different function from here on out.
Once down in the crypt, Arquen will ask the Night Mother where they should go from here. The Night Mother will tell her that Lachance was not the traitor and that the Black Hand is still tainted. At that point, Bellamont will kill Alor and Arius and try to kill the Night Mother. It must be scripted or something, but Alor and Arius go down with one hit each (they are both level 20) and Bellamont's dagger isn't THAT good (it only does an extra 5 points of Frost Damage). Bellamont isn't level 20, though. He's 20 levels higher than you, so it might take a while to bring him down, but Arquen is essential. Between the two of you, Bellamont should go down eventually. Once that's done, the Night Mother will promote you to Listener (all of her dialog options get you the same story with slightly different introductions) and the mission is essentially over.
I say "essentially" because there are still a few things that you can do. The first is to clean up any goodies in the crypt (some are decent, most aren't). On the slab with the skeleton is a Lichor ingredient. There are only three in the whole game, except for what you can collect in Mankor Camoran's Paradise (toward the end of the Main Quest) and whatever might be available through a mod of some kind (you get three Mana Bloom plants as part of the Wizard's Tower official mod). Lichor will not duplicate in the Archmage's ingredient chest, but it will respawn at the three places where it has been placed (here, the Anvil Mage's Guild and the Dividing Line in Leyawiin). Unfortunately, this is the only time that you can get into this crypt, so you might as well grab it while you can.
After you have cleaned up whatever it is that you want to take, talk to the Night Mother again, who will transport you and Arquen to the Cheydinhal Sanctuary and end the mission.