This quest is obtained upon arriving at Winterhold and approaching the beginning of the bridge to The College of Winterhold. It is the start of the College of Winterhold Questline.
Walkthrough
When approaching the bridge to The College, the guardian of the bridge Faralda will ask the Dragonborn to prove their ability to enter the College by casting a spell. The spell's level will depend on one's level and perks. If one does not know the spell, they can buy it from her for 30 . The Dragonborn must, however, possess enough Magicka to cast the spell she asks them to demonstrate, or raise the amount of Magicka by the use of an amulet, a ring, robes or another means. If one's skill is too low to cast even at the Novice Level, they will need to come back when they have leveled, and raised their Magicka enough. They may circumvent this test by passing a speech check, although the option to persuade may not be present unless one's skill is high enough. Alternatively, the option to say they are the Dragonborn can be chosen, and instead of a spell, they will be asked to demonstrate the Thu'um. (This is only an option when completing the quest Elder Knowledge.)
She will then lead the Dragonborn to the College and give them a quest to speak with the College leader Mirabelle Ervine (Master Wizard), a mage in the courtyard. This allows the Dragonborn access to The College of Winterhold. She will give some Novice Robes and a Novice Hood to wear if one chooses so. These robes will have an enchantment to make certain spells cost less. The set is basically the same as the first robe and hood the Dragonborn came across when escaping from Helgen Keep.
The Dragonborn will then be taken on a short tour of the College and be told to see Tolfdir in the Hall of the Elements where he is giving a lecture. Tolfdir is teaching three other students and the Dragonborn about the importance of safety while learning Magic. After a brief exchange with everyone, he decides to ask for the Dragonborn's help in a practical demonstration of ward spells. If one does not have a ward spell learned, he will teach them the Lesser Ward spell for free. Then they'll be asked to defend themself with a ward spell while he casts a long-range fire spell at them (either always a weakened version of firebolt, OR, it's possible the type and power of which is determined by one's level and one's ward spell's level). Once the Dragonborn has defended themself, Tolfdir will ask the class to travel to Saarthal to take part in an expedition.
Journal
Journal Entry
I've found the College of Winterhold, where mages study the arcane arts in Skyrim. If I want to learn more about magic, I'll need to join their ranks.
Objective: Join the College of Winterhold
In order to join the College of Winterhold, I need to show I'm capable of simple magic by casting a Magelight spell.
Objective: Cast a Mage Light spell
In order to join the College of Winterhold, I need to show I'm capable of simple magic by summoning a Flame Atronach.
Objective: Summon a Flame Atronach
In order to join the College of Winterhold, I need to show I'm capable of simple magic by casting a Firebolt spell.
Objective: Cast a Firebolt spell
In order to join the College of Winterhold, I need to show I'm capable of simple magic by casting a Fear spell.
Objective: Cast a Fear spell
In order to join the College of Winterhold, I need to show I'm capable of simple magic by casting Healing Hands on Nirya at the entrance to the College.
Objective: Cast a Healing Hands spell
I've been allowed to join the College of Winterhold, and need to find Mirablle Ervine for a tour of the grounds.
Objective: Report to Mirabelle Ervine
I have joined the College of Winterhold. Mirabelle Ervine has agreed to show me around in order to become familiar with the grounds.
Objective: Tour the College of Winterhold
I have joined the College of Winterhold, and after a tour of the grounds need to find Tolfdir, who looks after the new Apprentices.
Objective: Listen to Tolfdir
After joining the College of Winterhold and speaking with Tolfdir, I've learned a bit about wards and will be accompanying some of the others on an expedition.
Quest complete
Bugs
This section contains bugs related to First Lessons. Before adding a bug to this list, consider the following:
Please reload an old save to confirm if the bug is still happening.
If the bug is still occurring, please post the bug report with the appropriate system template 360 / XB1 , PS3 / PS4 , PC / MAC , NX / PS5 , XS , depending on which platform(s) the bug has been encountered on.
Be descriptive when listing the bug and fixes, but avoid having conversations in the description and/or using first-person anecdotes: such discussions belong on the appropriate forum board.
Click to see the list of bugs encountered
It is possible for an assassination attempt or a dragon battle to occur in the middle of your tour with Mirabelle (in the college courtyard), which will interrupt her scripted path and leave it unable to complete - she will resume her normal daily pattern and tell you "After I show you the grounds, we can talk" if you attempt to interact with her. Tolfdir's class in the Hall of Elements will not be triggered, so you cannot simply skip ahead; to complete the quest and continue the faction storyline you can go to Tolfdir, as the quest will automatically continue when you approach him.
When you're supposed to help Tolfdir demonstrate the ward spell there's a possible situation where he doesn't proceed with the spell casting even when your character seems to be standing in the right place, or he may ask you to sustain the ward spell even when it's already actively sustained. Based on this editor's experience, this is due to the trigger area for this scene being a very small and precise area, so when your character and/or including the ward spell they're sustaining isn't inside the trigger area, the game will not detect it properly. The line of sight to Tolfdir also need to be clear, so make sure your companion does not block the line of sight between you and Tolfdir. Also, If you release a housecarl while in this place, all the members of the room will immediately become hostile towards him/her and attack. This will cause this bug.
The trigger area is in the circle, stand on the left edge, try to face Tolfdir perfectly.
Your character is automatically standing in the trigger circle when Tolfdir speaks to you. When he says "Just stand over there," Don't move. Just look at him and hold the ward spell till he casts his spell at you.
Also, sometimes when you tell Tolfdir that you learned the spell Lesser Ward already, he does not proceed with his explanation/demonstration, but instead acts as a normal character not bounded into any quest, so tries to sell his books/ robes to you, even if you try to proceed with the demonstration. He is also going to follow you everywhere and is automatically starting a conversation with you; he does not follow you into areas outside the Hall of Elements and stays with the students if you walk away from him faster.
To FIX: When Tolfdir first moves into position and asks you to stand across from him, move into position facing his character and try slowly stepping backwards or shifting sideways towards the left or right until you're in the right spot and the quest proceeds. If this fails, walk behind Tofldir and kill the students behind him. When this is done, run away from hostile people and fast travel to another town. Go back to the college and Tolfdir will talk about how unfortunate events occurred, and the quest will be completed. Once he asks you to cast the ward spell, if he stops casting his spell halfway and tells you to sustain the ward spell even when you already have it going, do the same thing and shift around until you're in the right spot and he proceeds to cast his spell. Make sure to do this while facing the proper direction (towards him), and while you're actively sustaining the ward spell. Otherwise it can be hard to find the right location. Note that ANY type of ward spell will work here, so if you have trouble sustaining the spell due to lack of mana, be sure to choose the lowest level spell (Lesser Ward), and use potions, enchanted items and other things to temporarily boost your mana. Your companion/s generally do not affect the completion of this sequence, but if you wish to avoid any complications (such as them getting hit by standing in the wrong place), you can tell them to wait in a safe position inside the same room. If all else fails, you can "complete" this quest and auto-start the next one "Under Saarthal" by typing console command "setstage Mg01 200".
Another way to get past Tolfdir not starting the demonstration is to use Unrelenting Force on him.
Sometimes Tolfdir won't continue if you've only equipped the Ward spell to one hand. Make sure it's equipped in both when you cast it, and cast it with both. Only then does he continue.
Not having a weapon equipped in non-casting hand seems to help fix the bug.
If you are "hiding" in the entryway out of sight and use your bow to take out a fellow student, then exit undetected, you can skip to the next quest without paying a bounty.
If none of the above work, kill one of the new recruits. Onmund is the least-important. Then, run out of the College, pay the bounty to a guard and go back to the Hall of Elements and talk to Tolfdir.