Morrowind:Telvanni Hortator

Quick Walkthrough
# Meet with Master Aryon in Tel Vos (Upper Chamber) to receive an overview of the Telvanni councilors.
# Get Aryon to vote for you as the Hortator.
# Convince Mistress Dratha in the Upper Tower in Tel Mora.
# Convince Master Neloth in Tel Naga (Sadrith Mora).
# Convince Mistress Therana in the Upper Tower of Tel Branora.
# Convince Master Baladas in Arvs-Drelen (Gnisis) if necessary.
# Kill Gothren in the Upper Tower of Tel Aruhn.
# Return to Master Aryon to be named Hortator of House Telvanni.

Detailed Walkthrough
Overview
This quest is part of convincing each of the three Great Houses to vote you as their Hortator. The exact order you do the houses in is not important. The House Telvanni portion of the Hortator quests is a bit different since in the end you can ultimately kill all the Telvanni council members instead of persuading them all (as is their custom for resolving disputes). Of course, this route is not the suggested one, but it is possible. In any case, if you are already the Archmagister of House Telvanni, you will become the Hortator as soon as you discuss the topic with Master Aryon.

It is highly recommended you acquire some means of levitation before undertaking this quest, as it is needed to reach all of the council members except Master Baladas.

Master Aryon
The Mouths in the Telvanni Council Hall will suggest that you first speak to Master Aryon in Tel Vos (just west of Tel Mora and opposite Vos). Aryon can be found in his chambers at the top of the tower, within the root-like structure that wraps around it. The easiest way to reach his door is to levitate; however, if your Acrobatics skill is very high (at or near the cap), you can alternatively climb to the top of the central tower and jump from platform to platform to reach it, or simply head out the back door of the Barracks and Armory and jump directly to it from there. 

Upon talking to him, he immediately affirms his vote for you being the Hortator. If you are the Archmagister of House Telvanni, this alone is sufficient to make you Hortator; otherwise, he also tells you about the other council members that you must convince to get their votes. Master Neloth is ill-tempered, Mistress Dratha doesn't like men, Mistress Therana is losing her mind and Archmagister Gothren will probably delay his vote indefinitely. Aryon recommends that you kill Gothren, admitting that he stands to gain from the Archmagister's death. He tells you his advice is still good, and, as detailed below, it is.

Mistress Dratha
Mistress Dratha is found in the Upper Tower in Tel Mora (just east of Tel Vos). If you're playing as a female you'll get her support right away. If you're a man however, you'll need to raise her disposition quite a bit to get her to support you (80 or higher). If you're a man and not a member of House Telvanni you will need to raise her disposition by using your Speechcraft (61 or higher) to persuade her or bribe her with lots of gold, or otherwise kill her. If you can get her disposition high enough, you can Hurl yourself at her feet and plead for a hearing. After you get her vote, she will also throw in four Summon Golden Saint scrolls if your character is female; just one if you are playing a male.

Master Neloth
Master Neloth in the Upper Tower at Tel Naga (you will need to levitate to get to it) in Sadrith Mora will give you his vote for Hortator if you raise his disposition high enough (70 or higher).

Mistress Therana
Mistress Therana is found in the Upper Tower of Tel Branora, which is on an island at the far southeast corner of the game map (you can reach it by boat from Sadrith Mora, Molag Mar, Ebonheart, and Vivec). Talking with her will cause her to tell a long and irrelevant story. You can interrupt her by amusing her if you have a Speechcraft skill of 30 or higher, or you can successfully interrupt her with a story of your own if her disposition is 80 or higher. All other actions will result in failure.

Master Baladas
If you are a member of House Telvanni and have done the quest to convince Baladas Demnevanni to join the Council, you'll have to ask him for his vote as well. Master Baladas can be found in Arvs-Drelen in Gnisis and will give you his vote if his disposition is 40 or higher. Otherwise you will have to raise his disposition again before he gives you his support. Don't worry if you killed him after persuading him to join the council as the game will treat the situation as if he never joined.

Gothren
Gothren can be found in the Upper Tower of Tel Aruhn, just west of Sadrith Mora. Unfortunately, unlike the other council members, no matter what you do to persuade Gothren, he won't give you a decision, forcing you to kill him as Aryon suggested. If you raise his disposition high enough, he will eventually give you a direct refusal. This is no easy battle as Gothren is a master spellcaster and he has two Dremora guarding him. Gothren has a spell called '''Gothren's Gout''' that paralyzes while damaging you, so some equipment that resists paralyzation or gear that gives 100% magicka resistance is helpful. If you get a few good surprise hits in with a powerful weapon, or paralyze him, he won't have much time to cast anything.

If you have the means, command one of the Dremora protecting Gothren. This way, Gothren will kill it for you while still taking damage himself from his own ally. You can then kill the other Dremora (or take control of it) much more easily before turning fire to Gothren.

Alternatively, attacking either of the Dremora flanking him will cause all three to attack you without the other tower residents joining in. Taunting Gothren will have the same result.

Becoming Hortator
Any councilor (including Therana) can give you the title of Hortator once all surviving councilors agree, even with Aryon dead. However, to get the Robe of the Hortator you must go to Aryon and tell him you have obtained all the votes - if Aryon is dead, the robe will be in a crate near the entrance to his chambers.

Notes
While you are in Tel Vos, check the northeastern Tower. Look for a hidden door on the second landing from the bottom of the staircase. This will lead to a trapdoor which in turn leads to a small room with Azura's Servant (an enchanted Daedric Shield), an enchanted spear and an axe. Be aware that a powerful creature guards this room.
In the Upper Tower at Tel Naga there are several locked/trapped golden doors. You are free to pick these without consequence, and one contains a leveled set of Alchemy Apparatus.
If you plan on joining House Telvanni later, be aware that killing Gothren will prevent you from doing either of Mallam Ryon's quests.

Quest Stages