When you find the ruins, Larienna should be waiting by a campsite just outside the entrance. Approach Nchurdamz from the north, on the mountaintop, not from the west and the water (the campfire near there is a trio of hostile Ashlanders). Talk with her, and she'll tell you she is hunting a wounded Daedroth named Hrelvesuu. The ruins are small and filled with a variety of robots to take care of. If you make it to the lava room, you should find a key to the locked (60) and trapped doors to the west. Behind the doors you should find the Daedroth that must be killed and, once it is dead, Larienna will stop following you. You can be healed a little by her if you talk to her after she joins you.
Each time you tell Larienna to wait, her disposition towards you drops by two points.
Hrundi's dialogue implies that you will help Larienna clear out necromancers from Nchurdamz, there are no necromancers to be found, however.
If Larienna dies during the quest, Hrundi is disgusted but there is no penalty. Obviously, there is no reward either.
This quest is one of the few for which specific dialogue was recorded:
"Hrelvsuu! [sic] I have come for you! Show yourself!"
"I can smell the stench of the Daedroth. It is here and I will find it!"
"The beast is near now ... very near. Be on your guard."
"At last! A means to vanquish Hrelvesuu. The final battle awaits!"
"Hrelvesuu is vanquished, yet somehow I feel uneasy. I must investigate these ruins further. You have been a worthy companion. Farewell my friend."
Whenever you ask Larienna to heal you, she tells you that doing so weakens her. In fact the only effect on her is the expected Magicka expenditure of casting a weak Restore Health spell.
Larienna uses an area-of-effect Shock Damage spell that can kill lower level-characters in a single casting. Since she does not show discretion regarding when she casts it, be sure to keep distance between you and the enemies as long as she has Magicka left.
After finishing the quest, Hrundi will tell you that Larienna has left Vvardenfell because of "unfinished business". Despite this, she will actually still remain in Nchurdamz. You can return to her for additional minor healing if you're in the area again later.
Quest stages 23 and 55 (see below) are never set, and appear to have no effect when set via the Console.
You might not get the last line of recorded dialogue upon Hrelvesuu's death, nor get a Journal update for the necessary quest stage 90 (see list below); and Larienna may not stop being a follower-mode NPC. Yet you may have a soul gem with Hrelvesuu's name on it proving that the job was done. Larienna will continue to respond with "What's that? Do you require aid?" as if you've stopped in mid-hunt to ask for healing.
This bug seems to be triggered when she is fighting Hrelvesuu alongside you and it is your blow or magic that actually kills the Daedroth. But it may be a matter of more subtlety (perhaps soul-trapping, or something to do with NPC fight-cessation timing).
Use the Console (see below) to repair your game with the missing stage 90 entry if this happens; there is no other fix. Even this will only update your Journal to record the death of Hrelvesuu without that of Larienna.
If Larienna remains in follow mode (likely), you need to find a way to ditch her, without her dying by following you around into danger like the nearby Daedric shrine. Just doing Almsivi/Divine Intervention or Recall from the Hrelvesuu room is an easy way, though if you wish to continue on foot, another option is Locking her in Hrelvesuu's room, which requires locking both halves of its double door, or using Invisibility to leave Nchurdamz without her noticing. Larienna's proper dialogue states that she wants to remain on-site, anyway.
Trying to lead her back to Hrundi is a waste of time; she has no "rescue me and lead me to a safe place to complete a quest" scripting like various damsel- or gent-in-distress NPCs. She would continue to follow you around, though this would likely be harmless after reaching quest stage 100 with Hrundi; a free "bodyguard" for a while.
A Console fix to get her to stop following: "Larienna Macrina"->AIWander,0,0,0