You must be at least 5th level to be offered this quest and must have completed the Courier Quest. Talk to Mynisera again and she will give you a letter to Gortwog.

The opening dialogue for this quest is one of the flakiest in the game. You probably talked to Morgiah and did her quest long before tracking down Mynisera (it was Morgiah who told you to talk to Mynisera in the first place -- remember?), yet the developers use dialogue that implies that you haven't talked to Morgiah yet. Go figure.

Anyway, Gortwog wants to create a free and neutral orc state. Mynisera's letter tells Gortwog that she will support him in his bid if he will give you the Emperor's letter. Gortwog is willing to let you have the letter, but you have to go get it from where ever it is in the bowels of Orsinium. (What? You thought he'd just hand it over to you? Yeah, right.)

Gortwog is in the first big room when you enter Orsinium. If your Orcish skill and Personality are high enough, the guards will leave you alone (sort of). Otherwise, they'll attack you. There are three guards in the room: an Orc, an Orc Warlord and an Orc Shaman, plus an Orc who may or may not come through the door behind Gortwog. At lower levels the Orc Shaman can be pretty tough. They like to fireball you a couple of times and/or turn invisible and try to backstab you. The tables in the room will prevent the backstabbing (because he can't get to you). The Orc and Warlord should be no great shakes. Gortwog will be personable enough and will give you permission to retrieve the Emperor's letter.

Go through the left door at the back of the room (the one the Shaman is in front of). Opening the door will set off an alarm, alerting the critters that you are on your way. If you can get the Shaman or another Orc to step in front of the door, however, it will open on its own without setting off the alarm and you can backstab almost everything in the dungeon since they won't know you're coming.
Go down the corridor (you'll run into your first Orc just around the corner) and through the door at the end.
Follow this new corridor, turning left (south) at the first intersection, until you get to a room. Go through the door on the other side.
Go down to the room with the hollow pyramid and jump into the fountain in the northeast corner. This will teleport you to the landing above the pyramid.
Go up the left (west stairway) and south. An Orc will probably come out of the first opening on the left. Follow the corridor and open the first door door on the right.
Follow the corridor beyond (some orcs and a giant will want to have a word with you while you're passing through until you get to the door at the end.
Go through two small caves (and their inhabitants) and keep following the corridor down.
Keep going down. Turn right (west) where the corridor T's, then down, through the door and left (south) at the next T-intersection.
Keep going down until you get to a big room with a white pedestal in the middle of it. The letter will be on the pedestal and there will be 2 orcs in each of the rooms to the north and south. The doors open when you get close to the pedestal.

There is a door to the north that leads to a small room with a couple of treasure piles in it. You'll hear a strange sound when you step close to the pedestal. There is supposed to be an alarm that says "Stop! Thief!", but it doesn't' work very well.

The letter tells you that Lord Woodborne of Wayrest has the Totem of Tiber Septim, and Mynisera is supposed to use her influence to get him to give it to the Emperor (and here you thought he was having a torrid affair with one of his subject queens - well, actually he did, but it wasn't with Mynisera and the girl wasn't a queen at the time - more about this in another quest). So now you know that Lord Woodborne had the Totem, Queen Aubk-i knew he had it and that the Totem is missing. Guess who's got it. When you bring the letter to Mynisera, she'll tell you that Gortwog has probably circulated copies of the letter throughout the Iliac Bay, that the Totem should only be returned to the Emperor, and that the Totem will probably seek you out (you should be so lucky as to have it come to you).