This page offers a guide on how to pass the College of Winterhold Admission Test as well as how to complete the quest First Lessons.
College of Winterhold Admission Test
Speak to Faralda and tell her you want to join the College. She’ll tell you to cast a random spell from one of the five schools of magic. If you don’t have the spell she asks for, tell her and she’ll sell it for 30 Gold. Now the new objective is to cast your spell. If you’re still new to magic, you may not have enough magika to perform one of the spells she gives you.
Alternatively, you can pass a persuasion check to avoid the test, or say you are Dragonborn (if you’ve completed Dragon Rising). If you say you are Dragonborn, Faralda will ask you to use a Shout. Afterwards, whatever method you use, you’ll be granted access to the College. Follow Faralda all the way to the entrance of the College and once inside, you’ll see Mirabelle Ervine speaking with someone.
When she’s free, speak to her. She’ll give you the Novice Robes of Destruction, a hood that increases your magicka and some boots. If you’re a higher levelled character who typically doesn’t use magic you might find it difficult to transition to a novice mage since the enemies will be scaled to match your overall level - but I suppose that’s half the fun! If you want to live the authentic mage life, equip the novice robes and put away that sword and shield!
After Mirabelle has given you the new clothing, she will offer you a tour, so follow her around. First she’ll speak briefly about the Hall of the Elements, and then take you into the Hall of Attainment. She’ll show you your room, which you can use when you want to. There’s a lot of useful items in the other rooms in this area, so if you’re into stealing you can likely fill your pockets with some items of worth.
From here, she’ll take you back out and tell you to head into the Hall of the Elements to attend Tolfdir’s class. In here, open the gate in front of you and listen to what Tolfdir has to say. During the lecture, you’ll receive the ‘Lesser Ward’ spell, as Tolfdir wants to demonstrate it to the class, so equip it and keep using it until Tolfdir fires a spell on you. Afterwards, you’ll complete the first quest of the College.
Join the College of Winterhold