In order to gain access to the excavation site, the quest Under Saarthal must be started. This quest is started at 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. Reading the writ will start the quest Forbidden Legend. There is a Word Wall past Jyrik's chamber with a word of the Ice Form shout.