The lights are on
THE MAGES COLLEGE
When you fast travel to Winterhold, you will see the college. Trust me you can't miss it. When you go up the ramp, you will be greeted by a high elf named Faralda. She will not let you in the college unless you preform a task. The task varies depending on your level. She will request that you perform a spell, it may vary: Firebolt, Fear, Fury, Magelight, Healing Hands, Conjure Flame Atronach, Conjure Familiar, or Fireball. *Note; some of these spells need to be cast onto the seal next to Faralda or she will ignore your action, except for Firebolt and Fireball which will inflict splash damage to her and she will become hostile. Don't worry if you don't know the spell that she asks of you, she will offer to sell it to you for 30 gold. Once you have completed the task, the quest "First Lessons" will start .
Once in the college you will have to speak to one of the master mages named Mirabelle. She will be outside in the court yard beyond the two giant doors. She will be talking to a high elf named Ancano. You can listen in on the argument or you can skip it by talking to the Archmage Savos Aren (dark elf). After she has finished talking to Ancano she will give you a tour around the college: where you sleep, where you practice magic, and where you can meet the other students.
*All three students can become followers if you do small side quests for them.
After the tour you will meet up in the hall of elements where the other students are, while in the middle of a meeting. They are discussing that they should be allowed to practice dangerous magic if they want to. The other master mage is there. (there are multiple master mages, but only one is above them all, and that is the archmage, Savos Aren) His name is Tolfdir. He thinks that everyone should continue studying safety. Then tolfdir will ask you about your opinion. You can say "we should learn something practical" or you can say "safety is most important", it doesn't matter what you choose, both end up the same way. Tolfdir will show the class about safety, and use you as a test dummy. (what a thoughtful guy) He will cast firebolt at you and you have to counter it with a ward.(if you don't have one Toldir will give you one) After that the quest "Under Saarthal" will start and everybody will meet outside of the Saarthal entrance.
You will go in and tour around until Tolfdir tells you to go help the other mage thats exploring the site. The mage will tell you to find 4 artifacts; 3 rings and one amulet. Get there three rings before you get the amulet because you can disenchant them if you don't already have it. When you get the amulet you will be trapped in the room with no escape. The way out is to put on the Saarthal amulet and cast a destruction spell at the door. Then a hidden chamber will appear. If you follow the chamber Tolfdir will follow you.
You will be greated by a ghost in a small room. He will freeze time to speak with you. After that you will be attacked by draugr. Kill them and continue on. *Note: Tolfdir cannot be killed so don't worry about him. After the second chamber of draugr, Tolfdir will stay behind and you must continue forward. You will find some pillar puzzles that are quite easy.
Pillar Puzzle 1: There are 6 different movable pillars. The correct position for them is shown on the wall right behind them. They might be a bit hard to see, so using a candlelight spell or something similar can be helpful. Or use a torch.
After that you will find the next chamber where there is a Draugr Deathlord, Draugr Wight, or a Draugr Scourge (depending on your level), it will activate when you get near the top of the ramp you have to go up.
Pillar Puzzle 2: There are 4 moveable pillars. The corresponding animal to pillar is right behind them. But here's the thing about these pillars. They're linked to one or more of the other pillars. So when you turn one, one or more of the other pillars will move as well. This is not at random. Face the gate that you need to go through to know which pillars I'm talking about. Rotating the bottom right (southeastern) rotates itself and all three other pillars. The bottom left (southwestern) rotates itself and the top left (northwestern). The top left (northwestern) only rotates itself. The top right (northeastern) rotates itself and the both of the western pillars. (I know, this confused me to no end when I stumbled upon this puzzle)
At the end of the tomb you will meet a Draugr Deathlord that is invincible. Wait for Tolfdir to cast a spell on the big ball in the middle of the room. Then the death lord can be killed. Once dead search his body and take his amulet; this will start another quest "Forbidden Legend" (not part of the College of Winterhold quests). After that Tolfdir will tell you to go back to the college and talk to the archmage Savos Aren. Once done the quest is over, and the quest "Hitting the Books" will start.
*Note: Before leaving, there is a word wall where you learn the shout Ice Form