Skyrim Secondaries Intersection- Saarthal: Not Now, I'm Studying These Ruins

Whenever you're done talking to Tolfdir, be on your guard- he will approach where the Psijic mage was standing, and this causes two of the coffins in the room to burst open, releasing Draugr Wights.  Thankfully, Tolfdir is a very adept mage, taking a lot of the potential sting out of battle in the enclosed area.  Be wary of backing into walls, but you should overcome the undead here without too much trouble.  Once that is done, Tolfdir immediately turns and heads through the passage revealed behind the coffin opposite your entry to the room.

Check under the podium table here before following him- there's an Apothecary Satchel hidden under the ruined books and linen wraps that  holds some valuable ingredients.  Similarly, make sure you dig into the pockets of the corpse in the tunnel Tolfdir wanders into as you move to catch up with your teacher.

At the end of the tunnel, Tolfdir stops and waits, his way blocked by a porticullis.  Grab the obvious lever to open the thing, admitting the both of you to the large round room beyond.  Be cautious here, as the sarcophagi in the room are not just decorations...

Enter the chamber a short distance for the most safety, observing the terrain- the majority of the room is taken up by an immense pit (thankfully covered with a grate) that has a stone bridge crossing it and candle stands ringing its rim.  Tolfdir will proceed in with a surprising lack of caution, given his previous warnings to the other studends- or perhaps not so surprising given the power he shows during the fight.  Thankfully, of the ten or twelve coffins in here, only four or five of the draugr awaken, so the fight should be fairly short and easy.

Once the undead return to their rest (though somewhat less comfortably than before), Tolfdir wonders at the room- this is unlike any of his prior explorations in Nordic ruins, particularly with the large number of coffins.  He instructs you to continue on without him to try and determine what it is the Psijic Order contacted you about, while he stays to examine the room.  Loot the corpses for anything you want to take with you, and then use the two pull-chains bracketing the barred-off door to expose it- this is your path deeper into Saarthal.