In an alphabetical manner.
"The librarian arranged the books on the shelf alphabetically so they could be found easily."
In plain English: Alphabetically means arranging things based on their letters from A to Z, just like they appear in your dictionary or phone contacts.
"The library books are arranged alphabetically on the shelves."
The word alphabetically comes from combining the adjective alphabetical with the suffix -ly to form an adverb. It describes actions performed according to the order of letters in the alphabet.