How to Join College of Winterhold in Elder Scrolls Skyrim
The College of Winterhold in Elder Scrolls V: Skyrim is the equivalent to the Mages Guild from Elder Scrolls Oblivion. If you are a magic based character in Skyrim, it may be a good idea to visit the College of Winterhold as soon as possible. Many of the characters in the college can sell you destruction spells, conjuration spells, soul gems, and etc.
You may hear about the College of Winterhold from other characters located in other cities throughout Skyrim. Many of the barkeeps and inn keepers will tell you about the College of Winterhold if you ask. You do not need to ask about the College of Winterhold to join, however. You simply need to travel to the north by foot or horse.
How to Join the College of Winterhold in Elder Scrolls Skyrim
The College of Winterhold is in the northern part of Skyrim, in the vast snowy area. Winterhold is marked on your map at the beginning of the game, but you will not be able to fast travel there until you discover it. Set a marker on Winterhold and make your way there. The College of Winterhold is not in the town itself, but is close nearby - there is a bridge to the college. It is always snowing very heavily in Winterhold and not many people reside here.
Upon arriving at the bridge, a High Elf Wizard woman will stop you. Tell her you want to enter the College. She will ask you "why?". Answer the question however you want. She wants you to take a test to see if you have at least some small experience with magic spells.You can alternatively (persuade) her not to take the test, but you need to be good at speech.
Faralda wants you to aim a spell at the magic seal by her. Aim a magic spell at the seal to complete the test. If you have no spells, you can purchase one for 30 gold from Faralda. That is very cheap for an apprentice level spell!
Faralda will tell you to report to Mirabella Ervine. The first quest for the College of Winterhold, "first lessons", will be active.
Do not forget that Faralda has other destruction level magic spells you can buy!