Right from where we start, speak to Legate Rikke. She tells you you need to go to the outskirts of Korvanjund. Ok, but before that, lets do what Tullius said and go get our armor. Leave the Castle Dours and follow the marker out here...
Go right from the door you came out from through the arch and then left to find the armory.
He'll give you a full set of Imperial Armor. You also get to choose whether you want Light Armor for scouting, Heavy Armor for combat or something in between. Take what you want, then fast travel to Korvanjund or the closest point and make your way to the marker. Once here, you'll be approached by Hadvar, if you followed him back at the beginning of the game in Helgen...
Now speak to Legate Rikke and tell her that you're ready to move out. Approach the ruins and you'll be greeted by some Stormcloaks. Nothing to be afraid of, you will surprise the enemy and will easily outnumber them.
Note: With this many Legion soldiers with you, and Rikke too, it's impossible to lose, even at low levels. They could do ALL of the killing after all.
There's a MASTER locked gate at the bottom of this place that secures some gold and a chest. Open it if you can.
After killing off the welcoming party, go meet up with Rikke at the door and then enter the ruins. Grab the chest on the left and then sneak with your comrades and charge on the count of Rikke and kill the Stormcloaks guarding the entrance.
As you start going north and down, in the next big room more Stormcloaks appear. Now, as Rikke tries to go further ahead, she smells an ambush and it's time to find another route. From the entrance of this room, instead of going down, continue to the east and around to the north side. When you get to the next room, there's a Stormcloak standing on oil. If you can, shoot a Fireball to ignite the oil and burn him.
If you can't, follow this upper path and use Flames when you get to it. This will alert the rest of the Stormcloaks, but will make Rikke and the rest come in. Kill the remaining Stormcloaks and before proceeding, check the east side to find a chest as well as a skeleton holding a LIGHT ARMOR SKILLBOOK named "Jornibret's Last Dance". Loot it and now proceed.
In the next room, the Legion is surprised to see the corpse of a Draugr. Now simply follow the path and enter the Korvanjund Halls. There are some Stormcloaks in this first room, so take them out. As you go North in the next hall, there's a side tunnel going west with a swinging blade trap. Run across it; use the lever for them to stop and loot the chest.
In the hall, Rikke starts speaking. Listen to her and on the north side, you'll find some Stormcloaks dead and an Ebony Claw next to them. Examine the Claw using the menu and you'll see it has 3 symbols on the palm. This is the answer to the riddle on the wall:
Wolf (outer ring)
Moth (middle ring)
Dragon (lower wing)
Examine and use the Ebony Claw. Proceed and in the next room, you're told to look for a way to open the gate. Follow the northwest hall and on the upper floor, after the catwalk, you'll find a handle on the left side. Loot the place first and then use it. When you do, the Draugr will rise from their tombs. Ugh. Kill them ASAP and proceed into the Crypt.
In here, approach the Draugr Scourge sitting on the "throne" and examine it. It'll raise, and two more Draugrs will raise from the tombs. Ugh. Take care of the minions first, then focus all your attacks on the Deathlord (or lower level Draugr, if you do this quest early in your playtime). Loot the Scourge and take the Jagged Crown . Go to the south side of the room to find another Word of Power: Sand - Slow Time (or another of the "Slow Time" word variety).
And with this, leave the place and return to Tullius (use the ramp to the left of the word wall to get out quickly). Give him the Jagged Crown to end this Quest and start the next one.