There’s no out and out shortcut with this one, you basically have to just keep reading as many books as you possibly can, hoping that they give you a skill point. That means reading books on desks and in book cases for the most part. Remember, you can read a book without stealing it and getting caught for stealing, so go into people’s houses and read as much as you can without actually putting the book in your inventory.
It’s probably worth nothing though that the Hitting The Books mission from the Urag gro-Shub sends you to get books from Fellglow Keep and upon returning them Urag will give you a handful of skill books in return for successfully completing it (provided you’ve not read them elsewhere). There’s also a library in The Arcanaeum inside the College of Winterhold as well, where you’ll find skill books.
Thanks to jamby, there is a Skill Book Guide at the end of the trophy guide. Please see it for the complete list of locations.