This is a relatively lengthy side quest which involves finding 3 parts of an amulet from 3 separate dungeons, Folgunthur, Geirmund's Hall, and Saarthal. To start the quest, you must find a copy of the book Lost Legends. One can be found in the Dark Brotherhood Sanctuary, and one can be found inside the entrance of Geirmund's Hall, as well as several other places throughot Skyrim.
After opening the book, you will be prompted to "Investigate the Gauldur Legend." You will be pointed to a small campsite just outside Folgunthur, where you need to read Daynas Valen's journal. Go inside Folgunthur and find his body, his notes, and the ivory claw.
Fight your way through Folgunthur until you get to the first of Gauldurson, who is carrying the first piece of the amulet. Now you have to go to the other two dungeons, conveniently marked on your map, to find the remaining pieces of the amulet.
In Geirmund's Hall, you will go through basically the same process. Kill the Gauldurson and take the amulet fragment.
Unfortunately, Saarthal is under excavation by the College of Winterhold, andis locked up tight. You will have to complete the very short quest "First Lessons" by visiting the College and joining up. You will have to listen to Tolfgir for a moment, and he will start the quest Under Saarthal. Go back to Saarthal and after entering, he will tell you to help another wizard. This wizard will tell you to look for artifacts, marked on your map. When you take an amulet off the wall, you will have to equip it and then use a destruction spell on the wall you took it from.
This will open up a whole new part of Saarthal. Continue to explore until you get to the final Gauldurson. Tolfgir will disable his power so you can kill him and take the final piece of the amulet.
Now go to Reachwater Rock, the tomb of Gauldur. When you reach his burial room, you will have to fight all 3 sons again separately. They are a bit tougher this time, but if you alternate between your weapons and healing spells, they aren't too difficult.
Finally, Gauldur's ghost will reforge the amulet, which you can now wear. The amulet grants you +30 stamina, +30 magicka, and +30 health.