This is the alphabet of Classical Greek — that of Attica and Athens in the fifth century BCE. Clever classicists, glancing up from their Sappho fragments, dismissively tell us that this alphabet and its subtleties are well-established, and we trust them.
Then again, it Greek was a diverse language, and no two writers spelled everything quite the same way. Even modern scholars often differ in their pronunciation: there is an Oxford accent, a Stanford accent, and so on. Annoying, yes, but ancient Greek was primarily spoken, and you need to have an idea of how in order to produce some written forms correctly. Sorry.
Do not use modern Greek as a guide to ancient Greek. "Greek" has been around for five times as long as it's taken English to go from Geoffrey Chaucer to Hunter S. Thompson.
Uppercase lowercase: English name (Greek name): English word with approximate phoneme highlighted. Exciting notes!
Α α: alpha (αλφα): father.
Β β: beta (βητα): be.
Γ γ: gamma (γαμμα): go by default, but song before κ, μ, ξ, χ, or another γ. Our word
angel, for instance, comes from αγγελος (= messenger).
Δ δ: delta (δελτα): do.
Ε ε: epsilon (ε ψιλον — "plain e"): set. The lowercase form may be written either as two arcs or as a single arc bisected by a tick (i.e., either a backwards unbarred
B or a crossed
Ζ ζ: zeta (ζητα): z by custom, but technically misdeed. This means that Zeus (Ζευς) is pronounced something like
Η η: eta (ητα): fair. This is a mellower, longer sound than ε or α; it often ends words.
Θ θ: theta (θητα): thin by custom, but technically like loudly whispering too; that is, with a simultaneous or near-simultaneous hat.
Ι ι: iota (ιωτα): keen. This means that, for instance, π ought to be pronounced "pee", but don't trouble yourself.
Κ κ: kappa (καππα): kit.
Λ λ: lambda (λαμδα): loo.
Μ μ: mu (μυ): me. Think of the lowercase character as a stylized
M rather than a funny
Ν ν: nu (νυ): no.
Ξ ξ: xi (ξι): ox.
Ο ο: omicron (ο μικρον — "small o"): dot.
Π π: pi (πι): pip.
Ρ ρ: rho (ρω): rip by custom, but technically more like (Spanish) burro: rolled or trilled.
Σ σ ς: sigma (σιγμα): so by default and custom, but technically zoo before β, γ, δ, and μ. The alternate lowercase form, ς, is only used at the ends of words (see long s for an English equivalent).
Τ τ: tau (ταυ): to.
Υ υ: upsilon (υ ψιλον — "plain u"): something like French tu — between yes and boo; it's transliterated as both "u" and "y". This one bears watching.
φ φ: phi (φι): foo by custom, but technically a simultaneous or near-simultaneous pat and hi.
Χ χ: chi (χι): again, customarily chap, but technically a simultaneous or near-simultaneous keg and hip. When Anglicised, this generally is spelled
ch and pronouced
Ψ ψ: psi (ψι): oops.
Ω ω: omega (ω μηγα — "big o"): saw, with a little of so.
Diphthongs: two vowels sharing one accentuation (which will go over the second of them), or lack thereof, make a diphthong. It's just that easy!
Accents: vowels can be unaccented, grave (ò), acute (ó), or circumflex (ô). Accenting is fairly complicated, and belongs in some other node. Just try to put the most stress on the acute vowel.
Breathings: your keen eyes have already noticed that there is no hat sound in the alphabet, but that certain Greek-derived words (like "Hellenic", "rheme", and "hyper") start with that very sound! Ah-hah. When a vowel begins a word, it's given a semicircular breathing mark, which goes over it like an accent. If it's open to the left, ")"-like, it's a smooth breathing and nothing changes; if the opposite, it's a rough breathing and the vowel gets a ha sound before it. Thus, for instance, "Hercules" looks like "Ercules" until you notice the breathing. Rho (ρ), curiously enough, is always given a rough breathing when it rides point, but none of the other consonants bother. Want more? Go read Breathing marks in Greek.
Capitalization: inscriptions and other formal or constrained texts are generally put in all caps, and accents and breathings are left off. Otherwise, sentences do not take capital first letters, but proper names do. (Solitary caps in proper names are given accents and breathings, which float a little to the left of the letter.)
Punctuation: the question mark looks like our semicolon (";"), the semicolon like a raised period ("·"), and the comma and full stop like ours. You'll get along swimmingly; the language is more flexible in rhythm and emphasis, so it doesn't need as much punctuation. Usage is almost exactly what your English-honed instincts expect. (Since Greek is keen on parallelism and so on, you'll probably see proportionally more semicolons and fewer commas.)
You can find a tolerable rendering of Hellenic Greek (later than classical, but near enough for these purposes) halfway down http://www.linguistsoftware.com/gntu.htm.
Questions, suggestions, and corrections are of course welcome.
Unicoders: tell me how to render proper breathings and accents and I will make you a star. Thanks, Cogito! But on the other hand (as Cogito points out) Unicode font support is still weak enough that I'd better wait a bit.