You can get this quest by simply VISITING the ruins of Valthume (which are southeast of Markarth, southwest of Rorikstead, and west of the Cradle Stone Tower) and talking to the ghost in the vestibule named Valdar. Agree to help him destroy the Dragon Priest Hevnoraak and you'll have yourself a quest!
Before killing the Dragon Priest, we'll have to collect THREE vessels. Head inwards and enter Valthume proper. This first area is huge but uneventful, so take the right path downwards and watch out for a floor plate. Kill the Draugr you find and you'll see two paths (one is barred and is our shortcut out of this area). Continue on to a sitting area. The Draugr on the thrones are alive so you may as well sneak attack them. Also, the GRATED FLOOR here is trapped. I actually fell through it and there's spiders down below and the only way out is to pick an EXPERT LOCK, so be really careful.
Grab the chest and check the shelves of the room on the left for gems then continue on. Check out the room on the right for goodies, including a RESTORATION SKILLBOOK called "Withershins" on one of the tables. Continue on but beware of the oil on the floor with the fire pots up above. Kill some skeevers and check out the left rock door to use a handle. Follow this path and a high-level Draugr will fight you for the right to collect the FIRST vessel (the "Opague Vessel").
Once you have the vessel go back and continue past where the gate used to be. There's a wide-open area coming up with several Draugr in it, so be ready to fight. Unlock the iron door up on the second floor for a ton of potions and a chest, then go down to the ground floor. Before going on, check out the room to the left. There is a fake wall in here (the right wall) that you can open with a handle that leads to another chest and more potions. Head back now and continue on to the catacombs.
Right away you'll see a chest in this new area. It's trapped, and if sprung will release a GIANT SPIDER (who makes a GRAND entrance!). Continue on and fight through the catacombs, which are similar to every other Draugr catacomb out there (aka, be careful of "dead" Draugr coming to life). You'll come to a gate of iron blocking the path, but you can open it with a chain to the right. Inside of the room is another high level Draugr that you'll need to kill. After slaying him, be sure to grab the soul gems to the left (they spit fire at you later, otherwise) and grab the SECOND vessel (another "Opague Vessel").
Continue on after that and go further downwards. You'll fight more Draugr here both out in the open and form the walls. Also, don't let the giant spiked door thing hit you, eh? Pull a chain on the right to continue further. Keep going until you have to open a BIG door and kill some spiders. You'll see that there is an IRON CLAW on a pedestal. Grab it and get away to avoid some flames then go to the CLAW DOOR up ahead. Make the rings on that door match this:
TOP RING: DRAGON
MIDDLE RING: EAGLE
BOTTOM RING: WOLF
Past the door is a room with four Draugr in it. Be careful here as TWO of them (for me anyways) were DEATHLORDS. Kill them all and grab the FINAL vessel off of the stand. The gate onwards will open up and will let you learn a word from a DRAGON WALL. This one taught me SEEK - AURA WHISPER. Learn it and grab the chest, then continue on to be taken back to Valthume. Our objective now is to "Perform the ritual with Valdar". Valdar will be waiting for us in the first large room for you. He'll tell you to poor the blood in the sconce nearby and sit in the throne as he calls forth Hevnoraak.
Get ready to fight a DRAGON PRIEST before you do so. Hevnoraak is a powerful lich/wizard with lightning attacks. He can kill you in 2-3 hits if you aren't careful. Thankfully this area has lots of statues and other things to hide behind. Heck, when the fight starts, Hevnoraak has no idea you are even HERE, so use all of that to your advantage to beat him.
Afterwards, be SURE to loot him for the mask (called "Hevnoraak") and talk to Valdar. Valdar will thank you for killing Hevnoraak and this quest will now be complete.