First Lessons

Background
This quest is obtained upon arriving at Winterhold (City) and approaching the beginning of the bridge to The College of Winterhold.

Walkthrough
When you approach the bridge to The College, the guardian of the bridge Faralda will ask you to prove your ability to enter the College by casting a spell. The spell's level will depend on your level and perks. If you do not know the spell you can buy it from her for 30 gold. She will then lead you to the College and give you a quest to speak with the College leader Mirabelle Ervine (Master Wizard), a mage in the courtyard. This allows you access to The College of Winterhold. She will give some Novice Robes and a Novice Hood to wear if you choose. These robes will have an enchantment to make certain spells cost less. The set is basically the same as the first robe and hood you come across when escaping Helgen's Keep.

You will then be taken on a short tour of the College and told to see Tolfdir in the Hall of the Elements where he is giving a lecture. Tolfdir is teaching three other students and yourself about the importance of safety while learning Magic. After a brief exchange with everyone, he decides to ask for your help in a practical demonstration of ward spells. If you do not have a ward spell learned, he will teach you the Lesser Ward spell for free. Then you'll be asked to defend yourself with a ward spell while he casts a long-range fire spell at you (either always a weakened version of firebolt, OR it's possible the type and power of which is determined by your level and your ward spell's level). Once you have defended yourself, Tolfdir will ask the class to travel to Saarthal to take part in an expedition.

Bugs
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 peaople and fast travel to another town. Go back to the college and Tolfdir will talk about how unfortunate evnts 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". Not having a weapon equipped in non-casting hand seems to help fix the bug.
 * 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. 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 egde, 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 proceeed 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
 * Another way to get past Tolfdir not starting the demonstration is to use Unrelenting Force on him.
 * You can also use the Spellbreaker shield instead of a ward when you and Tolfdir demonstrate the ward spell.S