In order to gain access to the excavation site, the Under Saarthal quest must be started. This quest is found in The College of Winterhold, which can be entered easily after completing the very short First Lessons quest, regardless of magic skill. After that, Under Saarthal can be started by speaking with Tolfdir after his magic demonstration.
Defeat Jyrik Gauldurson in Saarthal, by the orb, and take his Writ of Sealing and his Gauldur Amulet Fragment. Read the writ to start the next quest point. Then, go to the Arcaenum and read the book Lost Legends to get the next clue about the origin of the Gauldur Amulet Fragment. There is a Word Wall past Jyrik's chamber with the Ice Form shout, "Flesh."