New primary objective: Retrieve the fragments of Wuuthrad
New optional objective: Wipe out the Silver Hand
Leave the Jorrvaskr sanctuary, open the world map and look for Driftshade Refuge (screen above). This place is located in the northern part of Skyrim. If you haven't unlocked it yet, it would be good to start your journey in Dawnstar, heading south-east. Plan your travel carefully, because you'll have to do some climbing. So I do not recommend choosing steep mountain slopes, because you'll only make your trip harder.
The Silver Hand headquarter you're looking for is located at the higher mountain (screen above) and after reaching this place you should deal with all local werewolf hunters. During this quest I strongly recommend exploring the area, to be sure that you've killed every opponent. Otherwise you may not complete an optional objective. After killing all enemies, use the small door and enter the Driftshade Refuge.
Head north. You'll encounter first group of opponents after getting to the quite large chamber (screen above). Remember to watch out for heavily armored enemies and quickly eliminate bowmen. After the fight use the western passage, because the northern door is closed. Be careful, because there are few more werewolf hunters in the area
Head west, continuing exploration of Silver Hand stronghold. New opponents await you in the next large changer. Kill then, explore the area and choose a corridor leading north. On your way you'll encounter a closed door to the western room (screen above) and if you want to complete the optional objective of this quest, you have to break in, because inside you'll find one Silver Hand member.
Return to the main corridor and keep going. Prepare to fight another battle after a while. Make sure that all enemies are dead and approach the eastern passage (screen above). Pulling the lever will give you an access to the door leading to Driftshade Cellar.
Head north. There are new Silver Hand members in this area and you can eliminate at least few of them by using the local trap, by stepping on the pressure plate at right moment (screen above). Examine cabinets here, with more or less valuable armor elements and then choose a corridor leading east.
Open the door to the next room and deal with a group of opponents there. After the fight I suggest searching for Light Armor skill book The Rear Guard. After exploring the area, choose the northern entrance to the ice cavern (screen above). Be careful because you'll be attacked by werewolf hunters with at least one stronger opponent. If you want, you can free local wild werewolf, but he will attack you anyway.
Head north now and attack another group of Silver Hand members. Again choose a corridor leading north (screen above). After reaching the next cellar room, prepare to fight with new enemies. Kill them all and choose a corridor leading north. Finally you should reach to the door that leads to previously unexplored part of the Driftshade Refuge.
Use the stairs and attack the last group of werewolf hunters (screen above). Try to eliminate bowmen first, so they won't bother you later. After the fight the game should credit an optional objective of this quest. If not, return to previous location and make sure that it is fully secured.
You may now explore current area. You will find here two valuable books: One-Handed skill book 2920, vol 01 - Morning Star and Block skill book Warrior. Examine also enemies' corpses, because at least one of them was using quite good sword. Finally approach the table, where you'll find Wuuthrad's fragments (screen above). Collect them all.
New primary objective: Return to Jorrvaskr
You can now choose the southern corridor (screen above). Interact with a bar so you can return to previously explored locations and you'll be able to leave the Driftshade Refuge. Open the world map and return to Whiterun. Vilkas should leave you here, mentioning the preparations for funeral. You can start next major Companions quest without any additional preparations.
Unlocked Companions quest: Glory of the Dead