Plutarch says:

καὶ τὴν μὲν Ἰλιάδα τῆς πολεμικῆς ἀρετῆς ἐφόδιον καὶ νομίζων καὶ ὀνομάζων, ἔλαβε μὲν Ἀριστοτέλους διορθώσαντος ἣν ἐκ τοῦ νάρθηκος καλοῦσιν, εἶχε δὲ ἀεὶ μετὰ τοῦ ἐγχειριδίου κειμένην ὑπὸ τὸ προσκεφάλαιον, ὡς Ὀνησίκριτος ἱστόρηκε

And as he considered and called the Iliad the way [ἐφόδιος is poorly translated into English, it means a path, or a way and means] of warlike virtue, and took with him Aristotle's recension and calling it the 'Iliad of the Casket,' he kept it always lying with his dagger under his pillow, as Onesicritus tells us

Strabo says pretty much the same thing, also calling it the "Iliad of the Casket." A νάρθηξ is both the name of a kind of plant that had a hollow, rigid stalk that could be used as a cane or a container (Prometheus carried fire within the stalk of one) or it can be the name for a little casket, often filled with perfumes and other toiletries.

During Alexander's lifetime the codex, with its familiar pages and binding, had not yet been invented, so all books came in the form of scrolls. Usually books were long enough to fill up several scrolls--it's from this that the division of works of classical literature into books originates. Within a single book of a work the text was arranged into columns of several dozen lines each--the size of these columns depended on the work contained, whether it was prose or verse, and what meter it was in. During Alexander's lifetime spaces between sentences, accent-marks, and punctuation were not employed yet in Greek--these innovations were apparently introduced at Alexandria. The books making up a single work would then be kept in a box all together, often with a little tag on each of the scrolls to identify whether that was Book One of Thucydides or Book Four.

Books were of course copied by hand, and we have references to the public sale of books as early as Plato, who has Socrates mention in the Apology that Anaxagoras' books could be bought in the "orchestra" for only a drachma (if the price was high). Large book collections are attested as early as Pisistratus, who was famed for his collection, but really big, important collections start appearing in the 4th Century, when the Athenians began churning out books like it was going out of style--Aristotle's library dates from this period. The βιβλιοπώλης, "bookseller," was responsible for their sale and production, presumably with a bunch of slaves copying stuff out for him. We have very little information on the price of books--Plato has Socrates say that all of Anaxagoras is no more than a drachma, and Martial says that a cheap edition of his poems is 6-10 sesterces, so a single book was well within the reach of an ordinary laborer, provided he could read it. Under the Romans bookselling was quite a large business, with booksellers established in major cities throughout the empire (at Rome they were particularly active in the Argiletum), and with private individuals or families undertaking to publish authors' works (Horace was published and sold by a family of booksellers called the Sosii, and Atticus maintained a staff of slaves trained as copyists in order to copy and distribute Cicero's works). But the book trade in antiquity was generally a private affair. Public booksellers are pretty well-attested, but intellectuals who had the inclination (and money) for large collections rarely actually bought their books. Instead copying of text was usually done as a private matter, either from the author directly (as many of the people building up large collections would know the author, they were intellectuals after all) or by borrowing editions from a friend. In either case you just had a slave copy it out for you and boom, you've got yourself a copy.

Alexander's Iliad, though, must have been an oddity, being small enough to fit into a νάρθηξ. It's a bit unfortunate that you've asked specifically about the Iliad, and in particular Alexander's personal edition of it, because the Iliad is sort of an oddity in ancient books in general. The Homeric Poems were orally-composed and at some point in the early Archaic Period or late Dark Age were committed to text--how exactly is unclear and isn't important for our purposes. You'll notice that Plutarch mentions that Alexander had a copy of Aristotle's "recension" (Ἀριστοτέλους διορθώσαντος ἣν), that is a revised and edited edition of the text. The Homeric Poems that we read today are not necessarily identical as those that Alexander might have read. For most of the Classical Period there were many different texts of Homer flying around, differing from each other ever so slightly (or sometimes differing quite a lot). This was a problem with all handwritten books even in antiquity and modern scholars still have to deal with it and decide what the correct readings are, but with Homer it was especially apparent already by the Classical Period. What we have today are descended from the products of the Alexandrian scholars of the Hellenistic Period, who reviewed the texts of Homer as they existed and drew up new recensions of them, but the text of Homer was not really standardized (and even then there are still mistakes in our manuscripts) until much later. There may have been an early attempt at a recension by Pisistratus, but there's not really any direct evidence for it--in any case Aristotle appears to have drawn up a recension of the text for Alexander personally. What this recension looked like we can't say, but it was probably done so as to make the text easily portable. The division of the Iliad into 24 books was something decided on by the Alexandrians, and Aristotle need not have used the same divisions--and probably didn't, since it's a bit difficult to make 24 books portable. Whether these scrolls were just written with a small hand (not impossible--we have a fragment from around the same time of a scroll of Orphic mysticism that's written with letters only about 2 mm high) or what isn't really clear