The achievement unlocks when you read your fiftieth book. Books can be found on shelves, in chests, as a quest reward, and sold in two specialty shops—The Luminary Leaf in Rathir & The Arcadium in Adessa. The books do not have to be picked up to count towards the achievement. They do, however, have to be read. An unread book in inventory does not count towards the achievement. A book that was not picked up but read while in a chest or on a bookshelf does count.
How to read a book from a bookshelf or chest without picking it up: Check the bookshelf, chest, or hidden pile by pressing

as if to loot it, but do not loot it. Pick locks (or open with key) and dispel wards if necessary. If the contents in include a book, highlight it and press

to inspect it. Then press

again to read it. Press

to read the entire book. Back out with

. This conserves inventory slots. If the bookcase or chest is private property; reading the book is not a crime (even if a lock was picked or a ward dispelled, but taking the book is theft.
You will come across books at different locations with the same title. Each of these books counts as a separate read and adds to your count of books read. Skill books that confer a skill point when read also count towards the achievement.
There are several hundred books in Kingdom of Amalur so there's no shortage of opportunities. Moreover, two thirds of the requirement can be obtained by buying the books from
The Luminary Leaf in Rathir and
The Arcadium in Adessa. Buy the books, read them, and then sell them back to the bookseller or any other merchant if you want to speed up your progress towards the achievement.
The video below demonstrates reading books without putting them in inventory and shows the achievement unlocking when the 50th book is read:
Gallow's End where the Legend of Dead Kell questline takes place has the largest concentration of books in the game. There is a much higher probability that chests and hidden piles will contain books than elsewhere in the game. Moreover, the contents of these chests and hidden piles randomly respawn unlike chests & hidden piles in most of the rest of the game giving you the potential for an endless supply of books. Be wary, though, of picking up any books in an ancient language. They count as quest objects for the Translations quest whether or not the quest is accepted from the librarian in Gravehal Keep.
Caution: Unless you feel compelled to do the Translations quest, do
NOT pick up any ancient texts. These quest items can never be removed from inventory. There are 12 ancient texts in total. Even if you've maxed out your carrying capacity to 120 slots with backpacks, they would take up 10% of the available space. You would be stuck with them for the rest of the game well after you successfully complete the Translations quest. Note that, for reading purposes, the ancient books cannot be read until they are translated. So, if you want them to count towards the achievement, you must accept the quest from
Deirdre Gwint in the Gravehal Keep great library after it is built.