As you regain control, equip the Staff of Magnus and try entering the College. The maelstrom won't let you pass. Use the Staff to gain access by standing beside the magical barrier whilst holding down the fire button to activate the staff).
Now go inside the Hall of the Elements and a scene with Ancano triggers. After all the talking, it'll be up to you to defeat him. You will also have a partner with you during the fight.
Note: Your partner here can very. Personally I've seen Tolfdir, but don't be surprised if it isn't him.
When the Eye reopens, some Magic Anomalies will come out to play. Ignore them and leave them to your partner. You focus on Ancano. He's not that hard, but you have to be fast. Speak to Tolfdir as you kill Ancano and then Quaranir will appear. Speak to him and he and the Eye will disappear. This marks the end of the main College questline and as a reward you are now the Arch-Mage of the College .
Tolfdir gives you the - really powerful and useful - Arch-Mage Robe and the Key to Arch-Mage's Quarters. This is your personal house, which you get free (and it contains loads of potions and ingredients to create loads more)! Pretty sweet reward, right? Congrats on playing through the main College of Winterhold questline!
The Eye of Magnus
Complete "The Eye of Magnus"