Great House Strongholds

All three of the Great House factions have three stronghold quests. They all run at the same time and they all progress at approximately the same rate, even if you are not a member of the other two factions. Each Great House has its own location for its stronghold:

For my money, the Hlaalu stronghold is probably the most conveniently located and the Telvanni is the least, but they're all equally inconvenient for most practical purposes.

All strongholds go through four distince phases. The first phase is finding out that you need one and getting the necessary materials to begin construction. The "stronghold" topic should start appearing when you reach Rank 4 or 5. This will point you to the person who will be your quest-giver for the construction:

All three of them will need a "Construction Contract". You get this from Duke Dren in Ebonheart. Go into the Council Chambers, and look for some spiral tower stairs through an archway on the back wall. The Duke will be the Dunmer in the Ebony armor on the next floor. All you have to do is basically ask for it and promise to do well for the people.

In addition, each of your contractors will want something else to begin construction:

Once you provide the necessary materials (the construction contract and whatever other items or money are required), construction will begin and you have almost completed the second phase. The only other thing required is wait a few days for a "Your Journal has been updated" message that tells you to go see the contractor to follow up on your stronghold. Head out to the site, talk to the foreman (who will tell you that everything is going fine), and report back to the contractor. A few days later you'll get another "Your Journal has been updated" message and phase two is done. You can go check out your new digs.

At the same time that the foreman appears at your stronghold site, the competing houses are building strongholds at their sites. These sites' progress more or less mirror your stronghold's progress. So you can go talk to their foremen, but they won't really have anything to say.

Second Stage Construction

If you are Hlaalu or Redoran, your stronghold is habitable and populated by a couple of NPCs who will provide services. If you are Telvanni, you've got a big fungus ball with some roots and branches and no door or anything else. It's time for the next phase of construction, so go see your contractor.

Once those tasks are accomplished, wait a few days for another "Your Journal has been updated" message and the second stage of construction will be complete. The Telvanni stronghold will now be habitable and have a couple of NPCs to provide services.

Once the first construction phase is complete, you can go visit the sites of the competing strongholds. The house on Odai Plateau is called "Rethan Manor" (after Raynasa Rethan, one of the NPCs), the house at Bal Isra is called "Indarys Manor" (after Banden Indarys, one of the NPCs) and the house at Urvirith's Grave is "Tel Urvirith" (after Reynel Uvirith, one of the NPCs). You will have a quest to kill the leaders of the competing strongholds before you can become the head of your Great House faction. Until then, all NPCs on the grounds or inside are useless ("You should not be here") except for the competing leaders, who will be hostile and attack you.

Third Stage Construction

Once you are ready to become the head of you faction (and have destroyed the leaders of the competing strongholds), you must make a third expansion to your stronghold before you can be promoted. Back to the contractor you go.