Although you can do it elsewhere, this is where most players will start off their climb to the top in House Hlaalu. The person who doles out the quests is Nileno Dorvayn, located just inside the front doors of Hlaalu Manor. She is also the person to talk to about joining House Hlaalu. Just ask about "business" to get quests.
Elsewhere in Hlaalu Council Manor is Dondos Driler, the person with whom you will be dealing to build your stronghold.
If you are Human or Elvish, Dorvayn notices that your voice sounds exactly like a certain Redoran. Now it just so happens that this Redoran is dead and no one else knows it. What she proposes is that you impersonate this dead Redoran to get something for Hlaalu. To pull this off, she gives you a Redoran helm (you get to keep it) and sends you off to Ald'ruhn to talk to Neminda in the Redoran Council Chambers (the three doors in the Manor District).
So put on your helm, go talk to Neminda and use the code phrase "Orphan of Arnesia" to collect the package (with instructions to deliver it to Maar Gan). Deliver the scroll to Dorvayn, instead, and you're done with 500 gold in your pocket. Easy peasy.
If you are Khajiit or Argonian, you won't be offered the quest. Too difficult to hide the tail, I suspect.
Seems that a new alchemist is muscling in on Hlaalu's business. You're to go steal some of her notes an/or formulae and bring them back.
Aurane Frernis has a shop in the Lower Wasitworks of the Foreign Quarter. You'll find what you need in three locations: on a table in her shop, in a chest at the foot of her bed (locked and trapped, as you would expect) and in her personal inventory. Snag any one of them and report back to Dorvayn.
In addition to the 5-point boost to your faction rep, your reward is a 15-point increase to Dorvayn's disposition and a 25-point decrease to Frernis' disposition. How nice.
While you're in Vivec, Dorvayn suggests that you stop by and speak with Edryno Arethi. This is not Dorvayn trying to get rid of you. This is a pointer to another Hlaalu quest giver.
The business of Hlaalu is business, whether above or below the table. And the first rule of business is to do unto the competition before they can do unto you, even if it's a member of your own House.
Avon Oran in Suran apparently needs to be taken down a peg or two, so you're to go kill the Kwama Queen in the Inanius Egg Mine (it's just east of Suran on the other side of the mountains).
You have three ways that you can play this out.
The first is to treat it as a straightforward quest. Go to the egg mine, kill the Queen and report back. No fuss, no muss, and 500 gold in your pocket.
The second is to double-cross Dorvayn. Accept the quest and then go talk to Oran. Oran will give you 1000 gold to leave the Queen alone. You'll lose the 15 points of disposition you gained with Dorvayn in the previous quest, but you'll get 5 points with Hlaalu and 1 point to your overall rep.
The third is to double-cross Oran. Take his gold and then go kill the Queen anyway. You'll lose 30 points of disposition with Oran (which turns out to be a net loss of 10 since you gained 20 when you took his gold, but you'll lose 10 more each time you mention the egg mine to him in the future), but you'll get two 5-point faction rep boosts, two 1-point overall rep boosts, and you'll still get the 500 gold from Dorvayn (plus the 1000 from Oran). J.R. Ewing would be proud of you.
House Redoran is the main competition in the guar hide market. Hlaalu needs to convince the alchemists to buy hide from Hlaalu rather than Redoran and you're to start with Rolasa Oren in Vivec. You'll find her in the Upper Waistworks of the Vivec Foreign Quarter.
You have two ways to handle it: convince her or eliminate her.
If you can get her disposition up to 80, she'll agree to buying Hlaalu hides. Intimidation or bribery will work. I tend to favor bribery for the simple reason that the disposition boost is pretty much permanent, so she'll continue liking me and might be useful in the future. But Intimidation will get the job done.
If you can't persuade, eliminate. You'll get credit for completing the quest by taking this route, but you'll get no faction rep boost. Hlaalu and the Thieves Guild share the belief that unnecessary killing is bad for business. You'll also lose out on the 1000 gold reward for a job well done.
You're to deliver new orders to Bivale Teneran, a Hlaalu spy in Ald'ruhn. She's a clothier with a shop in the Manor District.
Deliver the scroll (it's in code) and she'll give you an Exquisite Shirt and Extravagant Pants for your troubles. You can collect your 500 gold when you report back to Dorvayn.
You can pick up this quest from Dorvayn or from Uryne Nirith at Hlaalo Manor. If you get it from Dorvayn, it's a Hlaalu quest and this is the point where it would show up. You can get it from Nirith at any time as a side quest.
Ralen Hlaalo has been murdered. You might have already stumbled over his body in Hlaalo Manor while retrieving Brandy for Sugar-Lips Habasi. You may also have already taken care of the killer while cleaning out the Council Club for Larrius Varro. If so, there is little else to do beside collecting your reward. If neither of these apply, then it's time to put on your trenchcoat and play detective.
To make your job easiest, your first stop should he Hlaalo Manor where you should talk to Uryne Nirith in her room on the second floor. She will give you the murderer's description, which you can then ask about around town. If you don't have the description thread, you're going to get two suspects: Nine-Toes (one of your Blades Trainers) and Thanelen Velas (Camonna Tong) at the Council Club. If you do have the description thread, Velas is going to be the obvious culprit.
Go kill either or both; it won't affect your reward either way.
There is a small hiccup with completing this quest. If you have already killed Velas, you will not get the 1-point overall reputation boost. But you will get your 10-point faction rep boost and 1000 gold.
The East Empire Company out of Ebonheart is not happy with the high prices Hlaalu is charging for ebony, so they are threatening to start buying from House Redoran unless the prices come down. Hlaalu is not about to drop its prices, so your job is to sabotage the Redoran ebony mining operations.
Dorvayn gives you two choices on how to handle it. First, you can convince Canctunian Ponius in Ebonheart to continue dealing with Hlaalu. Second, you can kill Darns Tedalen at the Sudanit mine to shut down the Redoran mining operations. Or you can do both.
Dealing with Ponius is pretty straightforward. Get his disposition up to 75 or more and the job is done.
Taking out Tedalen is also pretty straightforward. To get to the mine, take the road that runs between Ald'ruhn and the Buckmoth Legion Fort east to the Ghostfence and then head south until you get to the mine. You'll find a lot of NPCs and a few guards in the mine, so you'll probably want to taunt Tedalen in order to provoke a fight and avoid any legal problems, but you could try to clean the place out (which won't help your rep with Redoran one little bit). There are tons of Raw Ebony laying around the mine, but they belong to Redoran. Steal them at your own risk.
If you convince Ponius or take out Tedalen, you get 1000 gold, a 10-point boost to your faction rep and a 1-point boost to your overall rep.
If you do both, you get 1000 gold, a 15-point boost to your faction rep, a 2-point boost to your overall rep, a Glass Cuirass, Glass Greaves and Glass Boots.
Dorvayn has no more quests after this.