Now speak to Delvin Mallory and tell him you found the map at the EETC. He'll give you gold for the map. Nice.
Leave the Guild now and fast-travel/carriage to Windhelm. From here, go northeast following the shore on the upper part of the mountain of course and soon enough you'll get to Snow Veil Sanctum. Mercer's outside waiting for you, so speak to him. Ask anything you want and head towards the entrance of the ruins (Mercer has a LOT of backstory to tell, so be sure to talk to him).
Mercer opens up the doors to the catacombs. Once inside, follow the halls into the first room, where there's a chest and two Draugrs that come out of the walls. Continue and when you start going north, look on the right (to the east) to find a locked door with Potions inside. You can always pre-emptively hit any Draugr you find standing up IN the wall too. Beware of bear traps RIGHT after the potion room!
Continue on north, killing all the Draugr that appear and when you get to a part where it goes around to keep going south, pull the chain next to the gate to open it (its on the left). After that, before going east when they want you to, open the door to the south and loot the urns and the chest that you'll find. Now go east and you'll fight SIX Draugr. Easy. Be sure to check out the table here for several potions and the SNEAK skillbook "Three Thieves". Continue on and in this larger room, you'll fight several more Draugr. Ugh.
After killing them all (should be rather easy), there are 2 sets of stairs. Take the ones on the southeast side until you come across a room filled with oil on the ground and an item in the center of it. Grab this Model Ship and the lantern will fall, burning everything. Grab the Model Ship and quickly sprint out of the way...
After surviving this, follow the second set of stairs all the way to the next area. Right off the bat and a few steps into this new room and you'll be fighting three more Draugrs. Kill more Draugrs as you proceed and before the gate blocking your path, you'll find two chests behind a trapwire with bones. If you trip it, you'll wake a Draugr each time.
Don't worry too much, loot the chests, activate the chain and proceed. As you start going south, Mercer tells you about the door up ahead hiding an ambush. Make sure you're ready, just like he says. Inside, you'll find several Draugr, and one magic user. Target the magic user first and take care of the rest.
Continue east now and follow the path until Mercer starts speaking about Karliah once again. As the door opens and you go inside, you faint and when you wake up, you'll see Mercer and Karliah speaking. Wow, good stuff. And now you're... dead. WHAT!?!?!?! Heh. This quest is now done and we start the next one.