Ε is our short e, as in get; never long ē.
Η, or ἦτα, was in ancient times always a long ē, English ā as in gate; now it is always ee as in seem or theme.
Θ is the English th, as in mouth, south.
Ι is always the slender English ee, either short as in peep or long as in scēne.
Ξ is ks, gs, contracted into x.
Υ, from which our y came, was in ancient times identical with the delicate ü, ue, of the Germans, halfway between οὐ = oo and ee, into which in the living language it is always softened, exactly as in some parts of Germany Brüder is pronounced Brēēder.
Χ is an aspirated k, but pronounced like milch in German or loch in Scotch, which the English, who do not possess this beautiful soft guttural, generally sharpen into a k, as in lake.
Ω, omega, as the name indicates, is simply a long o, as in πῶλος, a foal.
For the English h the Greeks used a simple mark of aspiration turned to the right thus, ἱερός sacred, pronounced hee-er-ŏs, while the same mark turned to the left, as in ἔρως, simply signifies the absence of the h. Whether this spiritus lenis, as it is called, was put on the initial vowel to indicate the presence of an original h which had vanished, I cannot say; but one can readily fancy that if the Cockney fashion of calling Highgate Igate were to become general, every such curtailed word might receive a mark thus, ’igate, as the survival of a lost breathing.
Besides the vowels in the alphabet we find in Greek, as in other languages, compound vowel sounds called diphthongs. They are seven—αι, ει, οι, αυ, υι, ευ and ου. Their ancient pronunciation is very difficult to expiscate, and in them we note the partiality of the Greeks for the slender sound of ee, called by a Latin writer gracilitas, and by modern scholars itacism. This tendency has wiped off the diphthongal character altogether from οι, υι, and ει, which are all pronounced like a single ι, English ee. To balance this, αι becomes the English ai, as in vain; ου retains its full soft roundness as in gloom; while in αυ and ευ in the living Greek the υ has assumed a consonantal value and become v, from which usage the εὐαγγέλιον of the Gospels has become the evangelium of the Latin Church, and the evangel of English; so αὐλός, a flute, is pronounced avlóss, and this v is aspirated into the kindred ƒ, when the following consonant is κ, π, τ, θ, χ, ξ, σ, or ψ, as in αὐτός, aftos, εὔξεινος, efxeinos. That the ancients, at least in poetry, did not do this is evident from the full diphthongal value of a long sound given to the εὐ in εὐαγής and such-like words by the dramatic writers.