As soon as you reach 3rd level, you will receive a letter from Princess Morgiah of Wayrest, asking you to come see her. It just kind of appears in your inventory. The letter tells you that she knows of your mission from the Emperor and has some information for you. So go to Wayrest Palace and talk to her. You can't miss her -- she's the babe in red at the top of the stairs. She'll want a favor before she'll tell you what she knows, so you have to deliver a letter to the King of Worms at Scourg Barrow in the Dragontail Mountains.
Scourg Barrow is in the southeast portion of the province, so you will need to move the map to find it. If you have the "Recall" spell, set your anchor at the entrance to Scourg Barrow (or even back at the entrance to Castle Wayrest) to make getting out a little faster. You can get out without it, but it makes life so much easier if you have it.
When you enter Scourg Barrow you will be in a room with 7 sarcophagi. The middle one on the western (left) side is the one you want. Open it and levitate or drop down.
The sarcophagus in the middle at the north end of the room opens a shaft that leads down to a room with two Mummies. If you are hard up for gold, you might want to take a peek. The only problems I have experienced with this are that the Mummies always want to stand directly underneath me (they can hit me, but I can't hit them) and the only way out of the room is via "Levitate", "Recall" or restoring a saved game. It's a general pain in the patootie, so I usually pass on that one.
Follow the corridor until it ends in a door. There will be two zombies on the other side. This a pretty tough fight for a low-level character, so you will want to save the game, just in case. Once the zombies are taken care of, go through the southern door on the west wall (that's the one immediately to your left as you enter the room).
Follow the passage on the other side of the door to a T-intersection and go left. (If you are really into exploration and want to fight a bunch of baddies, you can turn right at the T-intersection. It leads to the rift the Morgiah mentions in her directions.) Go into the cave and down. You will run into four bats. When you kill the fourth bat, look down and to your right. You should see a slope down. Take it. You'll some to a short T-shaped stone corridor. The door to the King of Worms' throne room is on the left in the middle of that corridor.
The door will be locked. You can pick it, cast Open on it or just bash it in. There is nothing on the other side that will hurt you, but it sounds like it. You can shoot arrows at the Vampire Ancients and Ancient Liches, but do it after talking to the guy in red. If you try to melee they will definitely fight back. It might not help your rep with the Necromancers any, but it sure helps your archery skill. Bring lots of arrows and a really good bow.
Once you talk to the King of Worms, he will give you a letter to deliver to Morgiah and you can beat feet.
You get back out the same way you got in (assuming you didn't anchor a "Recall" spell somewhere). When you get to the hole where you came down and if you don't have a "Levitate" spell, click on the tapestry on the left-hand side of the corridor. It will cast "Levitate" on you so you can get back up (you may have to click a few times to get it to activate for you). You can also climb if you want, but it's a little hairy finding just the right spot to climb up. Good for the climbing skill, though.
This place, by the way, is the headquarters for the Necromancers Guild. It seems to have been the original intent of the game to allow you to join the Necromancers, but it was not operative in the release version of the game. Perhaps in "TES3: Morrowind"? Only the developers know for sure.
When you return to Morgiah, she will tell you that an orc chief named Gortwog has the letter you need to find. She will tell you to talk to Mynisera, but to get to Mynisera through someone else. She doesn't say it, but the someone you need to go through is Mynisera's maid, Cyndassa, and you'll find her back in Daggerfall Palace. Morgiah will also give you a trinket for your troubles.