Organizing a personal library is not an innate skill for most children. Without clear instructions and modeling, even eager helpers are likely to stack and pile books in directions and categories that you never imagined. In the beginning, just focus on getting all the books right-side-up with their spines facing out. Then you can use the organizing process to build awareness of genres and/or alphabetizing.
To instill a sense of ownership and appreciation for your classroom or home library, let little readers label their books with fancy book plates. This makes book lending simple. Friends can share books and easily remember where to return the ones they borrow.
To get started, here are a bunch of cool, free printable book plates. Print them out on sticker paper, so you can snip them apart to use right away.

Get these sweet and summery illustrated
book plates from Issa at
Executive Homemaker.

Find this set of colorful, animal
book plates, designed by Shirley Ng-Benitez, at
Frugal Life Project.

Also take a look at these fairytale perfect printable
book plates from
Lizzy House.

I love the cool 3D-look of the
printable plates from
Squish, Suzanne del Rizzo's dimensional illustration blog.
Images from Executive Homemaker, Frugal Life Project,
Lizzy House,
Squish.