The Vowel Sounds
Notice that η, ι, and υ all have the same pronunciation in Modern Greek; ee as in see.
Note: There are basically 4 vowel sounds (ah, eh, ee, and o)
α - a as in father
ε - e as in met
η, ι, υ - ee as in see
ο, ω - o as in no

Vowel Diphthongs
These combinations are pronounced as a single sound.

αι - e as in met
ει, οι, υι -  ee as in see
ου - oo as in food
αυ - av before voiced consonants β, γ, δ, ζ, λ, μ, ν, ρ
αυ - af before unvoiced consonants θ, κ, ξ, π, σ, τ, φ, χ, ψ
ευ - ev - before voiced consonants β, γ, δ, ζ, λ, μ, ν, ρ
ευ - ef - before unvoiced consonants θ, κ, ξ, π, σ, τ, φ, χ, ψ
ηυ - eev - before voiced consonants β, γ, δ, ζ, λ, μ, ν, ρ
ηυ - eef - before unvoiced consonants θ, κ, ξ, π, σ, τ, φ, χ, ψ