The Iliad is written in a verse form whose technical name is dactylic hexameter.
In order to read it correctly, you must differentiate between long syllables and short syllables.
A syllable is long if it contains a long vowel (ᾱ, η, ῑ, ω, ῡ) or a diphthong (αι, αυ, ει, ευ, ηυ, οι, ου, υι, ωυ) or a short vowel followed by two consonants (ξ = ks and ζ = zd count as two consonants).
The basic verse unit is the dactyl, a long syllable followed by two short syllables, which in musical terms equates to a quarter note followed by two eighth notes. This metrical unit was called a dactyl because it resembles a finger (δακτυλος is the Greek word for "finger"), with one larger segment (between the knuckle and the first joint) followed by two shorter segments (the middle section and the fingertip). That image makes it easy to remember.
"Hexameter" refers to a line of verse composed of six "feet" or verse units.
Just as in music, where two eighth notes may be replaced by a quarter note, a dactyl may be replaced by a metrical unit which substitutes a single long syllable for the two short syllables in the second half of the dactyl. Such a unit is called a spondee, so named because ritual drink offerings (σπονδαι) in ancient Greece were performed to the accompaniment of slow, solemn melodies. The spondee slows down the rhythm in a solemn way.
(dactyl) = (spondee)
In musical terms, epic hexameter is three measures in 4/4 time, with the rhythmic beat falling on the first and third counts of each measure. Those beats are always quarter notes. The off beats (second and fourth counts) of each measure are either a pair of eighth notes or a quarter note, but the fourth count of the last measure is always a quarter note, slowing down the rhythm at the end of the line.
In theory, no variation is allowed at the end of the line. In reality, though, the final syllable may be either long or short. If short, it is lengthened by adding silence at the end (in musical terms, an eighth-note rest). So the poet can make the last foot either a spondee (two quarter notes) or a dactyl which has lost its last syllable and plays the role of a spondee (quarter note + eighth note + eighth-note rest).
Let's scan the opening lines of the Iliad and see how this plays out in the actual poetry.
Μη-νι-ν α-Ϝει-δε θε- ά Πη-λη- ϊ- α- δεω Α-χι-λῆ-ος
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dactyl dactyl spondee dactyl dactyl spondee
ου-λο-με-νη-ν ἥ μῡ-ρί' Α-χαι-οῖ-ς αλ-γε' ε-θη-κε
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dactyl spondee dactyl spondee dactyl spondee
πολ-λὰς δ' ιφ-θῑμ-ους ψῡ-χὰ-ς Α-Ϝι-δι π-ρο-ϊ- αψ-εν
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spondee spondee spondee dactyl dactyl spondee