Range weapons like bow and arrows, and magic spells are very effective against Morokei. Close combats like swords or axes can damage the priest too but will not be as effective. Also, avoid the shock spells that he’ll cast at you as these will deal severe damage on you.
At this point, Tolfdir (a non-playable character) will enter the same room and talk to Ancano. Wait for the dialogue to finish and for Ancano to paralyze Tolfdir before attacking.
Do not attack Ancano if the Eye of Magnus isn’t fully closed. Ancano is invulnerable to any form of attacks while the great sphere is open.
Ancano will occasionally try to open the Eye of Magnus again, making him invulnerable once more. When this happens, just repeat step 3 until the sphere is closed once more and Ancano is taking damage again. Any fire-type spell you’ve learned during the early stages of the game can also prove to be very effective against Ancano. Once Ancano is dead, talk to Tolfdir, who is now conscious, to continue with the quest.