Skill Books are unique books that grant a permanent one point increase to its associated skill. Opening a skill book will automatically grant the bonus. They can be read at any time and unlike Skill Trainers, who limit increases to five levels per level, there is no limit to the number of skill books that can be read in one level. However, the same book cannot give an additional skill bonus if read twice. The Dragonborn add-on includes an ability called Scholar's Insight that grants two points for every skill book read.
There is no tell-tale method to identify a skill book, as they often look identical to regular books. This can often lead to unknowingly raising a skill. Occasionally, the value of the book can be an indicator or the title can often allude to what skill it may be associated with - such as with Advances in Lockpicking.
There are five different books for each skill and a total of 90 books. They can be found almost anywhere and typically appear as a world item.
Given the rarity and usefulness of skill books, it's possible to add them to your inventory without reading them by ordering a follower to pick them up. The book can then be transferred into your inventory and read at a later date.
Twilight Sepulcher - shortly after completing the trial that requires the Dragonborn extinguish the torches on either side of the Nocturnal statue, take a left which leads them to a large room with a stairs down. The book is located on the desk among these.
Folgunthur, after entering and going down the stairs and into the first room continue through the passage and once through the passage turn left and on the wall will be the book with a dead adventurer and dead draugr.
Avanchnzel Animoncultory, just after the ghosts talking about setting up camp there is a side door. When you open the door step back as blades come out the ground. The book is sitting inside on a table.
Forelhost Crypt, go through the master locked iron cell in the middle of a room, down the stairs, through the underwater area to the north on the map. After coming out onto a dry room, go through the next underwater corridor and it will be in the next room on a shelf.