Note: If you don't know where the college is, you can basically ask just about ANY innkeeper "Where can I go to learn magic". This question will start the miscellaneous quest "Visit the College of Winterhold".
There's nothing quite as satisfying as wielding magic to suit your needs in Skyrim. Instead of a formal Mage's Guild, Skyrim houses the College of Winterhold, a place where aspiring mages go to learn, ouside the city of Winterhold. This questline will guide you through this place. To start it, you just need to visit the college.
First, head to Winterhold, all the way up in the North-East corner of Skyrim. Once there, go to the North side and you'll see a stone bridge. Before you can progress, one of the College Mage's will stop you and initiate conversation.