Online:Into the Outside

Quick Walkthrough
# Find Giruss in Riften by speaking to Itan-Nur on the lower docks.
# Go to Malsia's House south of Shor's Stone and activate the Skystones.
# Talk to Malsia.

Detailed Walkthrough
At Avanchnzel, an the corpse of an armored Dunmer named Solvar can be found outside the entrance. By inspecting it, the following observations occur:
: 
: 
:''"The target's name is Malsia. The Mages Guild wants her dead, something about her trying to open a portal. Whatever the reason, she must die."
: 
:"She's headed to Avanchnzel to gather Dwemer artifacts. Kill her when you find her. Be careful, she's handy with fire. Once the job is done, find me under the docks in Riften for your pay.
:"Signed, Giruss."
:I should look for this Giruss.

Giruss is located in a warehouse on the lower docks of Riften. An Argonian fisher named Itan-Nur can be found outside the door, and can be spoken to about Giruss. 
:"The fish have stopped biting for some reason."
:Where I can find Giruss? (grammar as written in-game)
:"Depends. Why are you looking for him?"
:I found a body I think he knows something about.
:"Go through the door behind me."
Giruss is found inside along with some mercenaries, where he can be confronted about Malsia. 
:"I don't know you. State your business and don't make me angry."
:I found your note about Malsia. Your assassin failed, but I'll take the job.
:"I already told the Mages Guild we tracked her to the house and she disappeared. Are you from the damn guild or are you just looking to die?"
:[Intimidate] Go ahead, threaten me again.
::"On second thought, here you go.
:If you feel that way about it, I'm leaving.
this will exit dialog. talking to him again will provide the same dialog options
:Just answer my question.

Giruss will order his mercenaries to attack you. Defeat them, then talk to him again.
:"Damn the Mages Guild. You can do your own dirty work from now on."
:Where's Malsia?
::"This map shows her house. We can't find her, but there's something set up in there. Go see for yourself."''

He provides you with a map to her location.

At Malsia's House, her journal can be found atop a nightstand. Read it to find out what happened to her:
: 
: 
:''"The guild's sent assassins after me. Now that I have the skystones, I must begin right away."
: 
:"If I reach the Aetherius, my soul may be torn from my flesh. The soul gem should protect me."
: 
:"The skystones may not be able to hold the portal open. Should they fail, I'll be trapped. But I'll take the risk. I must find where the portal leads."

There are three Skystones inside the house, mounted on Dwemer contraptions Malsia stole. They must all be turned (likely in no particular order), shooting out beams of light that meet to open a portal. Malsia will then emerge from Aetherius, where she can be confronted:

: 
:Malsia! Can you hear me? Malsia?
:'' ''

You are then rewarded with a staff called   and   Gold.

Notes
Though the jobs the Mages Guild instructed were to assassinate Malsia and retrieve the artifacts, neither of these are accomplished during the quest, and the player does not so much as report the outcome to Giruss. The warehouse where he was found cannot be entered again.
 

Quest Stages