This mod aims to fix that. You will go to the college, meet your instructor, and work your way to archmage-dom.
Upon entering the college in Winterhold you will meet Jordan Mhoram hanging out around the entrance to the Hall of Elements. Speak to him and he will charge you insanely exorbitant fees to take his classes. Upon payment he will provide you with books. As you progress in your spell abilities, you will be able to go back and speak to him again to start the next "semester". Once you have reached Expert level, he will direct you to the various masters of their individual schools in order to do the Master level quests.
You can specialize in one school of magic. As long as at least one of the schools has reached the next higher skill level, you can go back to Mhoram for more books. Technically you reach the apprentice level of a school when it reaches 25. However the minimum spell level (in any school) to get to the second semester in this mod is 30, since some skills start at or near 25 and it would be a tad immersion breaking to advance to the second semester at the same time you started.