Despite helping secure the town of Winterhold in the previous chapter, "Containment", Mirabelle does not know for how much longer they will be able to contain Ancano's magic. She wants you to retrieve the Staff of Magnus from Labyrinthian to use it against Ancano.

Open the quest journal:
The Stafff of Magnus
I need to retrieve the Staff of Magnus from withing Labyrinthian and return with it to the college of Winterhold. Only the staff will help me put an end to Ancano's abuse of the Eye of Magnus

Objectives
Enter Labyrinthian

The closest point to Labyrinthian is Morthal. Either fast travel there, or hire a carriage to get you there. From there, go Southeast to reach Labyrinthian. Locate the stairs on the side of the mountain and climb that road to Labyrinthian. Defeat the trolls in the area, and keep climbing until you reach the Ceremonial Door. Open the foor using the Torc of Labyrinthian Mirabelle gave you earlier.  Talk to the ghost of Savos Aren and the other ghosts, but they will ignore you.

Your goal now is to find the Staff of Magnus. Go through the Iron Door to the North. Activate the lever and immediately pass through the gate before it closes.

There will be a difficult battle in the next chamber. A Skeletal dragon, surrounded by skeletons! The best strategy to defeat them is to run to the other corner of the chamber and pull one of the skeletons to you. Kill the skeletons first one by one, then deal with the dragon. Use the pillars for cover. When the dragon dies, note that he wont release a soul, but he does have some valuable dragon bones on him so remember to loot it.

Head down to the East, into a chamber with an Etched Tablet in the center. The mages' spirits are talking on how they lost Girduin in the previous room, and decide to keep going despite the danger.

Go down and enter the Labyrinthian Chasm to the south. Go down. To the west, a loud roar will come from the door, so loud it will drain your magicka out.  The door is blocked by ice. Use a Flames spell to melt it and open the door. If you do not know the flame spell, head south and locate the spelltome on the pedestal.

Go west through the door you just opened. As you descend, the voice will sound, draining you from magicka again. Some Draugr will attack you. They are susceptible to flames, so use that against them. Go through the tunnels and arrive at an iron door. It has an electric trap on it so watch out. On the desk find a Spell Tome: Equilibrium. Learning this spell will allow you to convert 25 points of health into Magicka per second. You can be killed by this effect, so use with care. There is also an alchemy an enchanting station in this room you can use.

Go back up, and use the ramp to go down the chasm. Go down the stairs into a room with some shelves, and through a wooden door to the east. Follow the stream of water to the  Labyrinthian Thoroughfare to the North. Then open a gate to the west and enter a cavern with some Draugr. Unlock a gate with a novice lock to the  west. (If you dont have a lockpick, you can instead take a longer route around it). Reach a broken bridge. Drop down and follow the running water.

Defeat the troll in the next room, then  go north. Cross the bridge to the  west for some treasure (its guarded by a troll). Then go back across the bridge, and turn north to the gate. Activate the lever to open the gate and go through. Reach a door sealed with fire. Use an ice base spell to open it. You will now run into the spirits again, who have lost another one of their own. Aren urges them to keep going.

They will head down some spiral stairs. The stairs are sealed, so you cannot follow them. Instead, stand on the grate in the end of the tunnel (where the water is falling) and open the trap door. Drop down to the pipe then onto the ground. Then, defeat the enemies there and go west and reach a door into the Labyrinthian Tribune.

Go through the tunnels. You will find a pedestal with the spelltome Steadfast Ward on it, so learn it if you don't know that spell yet. There's also a chest with some treasure. Go down east.

You will find a corridor full of traps. The source of the traps are the soul gems on the pedestals, so you can remove them to deactivate the traps. You could also use the steadfast ward to shield yourself. Or use the power word whirlwind sprint to get to the end of the tunnel and immediately turn to the right and climb the stairs.

Work your way through the tunnels to the west. Enter a corridor. To the south, there is an adept lock with some treasure behind it. Continue west. Go through the iron door. Defeat the Draugr overlord inside it, and approach the glyph to learn the power word Time, Slow Time.

Keep heading west, defeating the enemies on the way. The mysterious voice will drain you from magicka here and there, so prepare potions or take cover until you restore your mana. Head west into another chamber where only three spirits remain now. Go south, and through the Iron Door.

Your goal in here is to defeat Morokei. At first he is invulnerable. Two Thrall Wizards are performing a ritual, feeding energy into a barrier. Kill them, and Morokei will materialize. Then kill him. Use the terrain for cover and vantage as necessary as this is a tough fight. Once you have killed him, grab the Staff of Magnus from his corpse. The Staff of Magnus can absorb 20 Magicka per second. If the targeet is out of magicka, it absorbs health instead. Feel free to equip it. He also has a mask, Morokei, which lets Magicka regenerate 100% faster.

Leave through the door to the East, not before looting all chests in the chamber. You will encounter the spirit of Aren for one last time, who promises to seal the whole place away. Your goal now is to get the staff back to the college at once.

Raise the bar on the door and go through, activate a lever to open a gate. You will run into Estormo, a Thalmor agent, who will tell you Ancano was right, you are dangerous. He wants to take the staff away from you and kill you. Defeat him, with the help of the Staff of Magnus, then climb the stairs near the crypt, raise the bar on the wooden door, and climb the ladder up to Skyrim. Fast travel, observe that you can no longer fast travel to the College of Winterhold itself, only to the town of Winterhold. From town, make your way up to the college. If you encounter a force field you cannot pass, use the Magnus staff on it to dispel it.

Tolfdir is standing outside with Faralda. If you ask him where Mirabelle is, he will tell you she did not make it. She stayed behind to buy time and let everyone else excape. Ask him why they are out there and he will tell you Ancano's power is growing and that they did not stand a chance. Tell him you are going in.

This complete the quest "The Staff of Magnus" and begins the quest "The Eye of Magnus"