Alright, here's my Greek alphabet guide for ancient pronunciations, along with the appropriate modern transliterations. Some of the transliterations don't make sense from an ancient pronunciation perspective - for instance, making aspirated t "th".
Α α - Open front unrounded vowel. We don't have this in General American. In practice, it's common to approximate it with the a in cat, but you'll unfortunately sound like an idiot if you do that. It should be fully open, while the a in cat is near-open. Maybe something in between the "a" in "cat" and the "a" in "father" - Transliterated "A"
Β β - b in boy - Transliterated "B"
Γ γ - g and gg in gaggle - Transliterated "G"
Δ δ - d in daddy - Transliterated "D"
Ε ε - "e" as in "feather bed" - Transliterated "E"
Ζ ζ - zd like in mazda - Transliterated "Z"
Η η - ai in hairy. Basically, a long e, which we don't generally have in English (no, ee in feet is not the long ee I'm talking about). - Transliterated "E"
Θ θ - t as in tat - Transliterated "TH", mainly because the modern pronunciation is an unvoiced th, as in "thin", but the ancient pronunciation was an aspirated t. It's virtually impossible for a person who grew up speaking English to tell between an unaspirated t and a d (which is a voiced, unaspiraterated t), as an irrelevant bit of trivia.
Ι ι - ee in free - Transliterated "I"
Κ κ - k in kiss (technically, k in English is aspirated, but you are never going to be able to tell the difference, because you weren't borning speaking the unaspirated version) - Transliterated "K"
Λ λ - l in let - Transliterated "L"
Μ μ - m in him - Transliterated "M"
Ν ν - n in nice - Transliterated "N"
Ξ ξ - ks, like the x in exist - Transliterated "X"
Ο ο - aw, like the o in doll - Transliterated "O"
Π π - p as in pipe - Transliterated "P"
Ρ ρ - "trilled r" as a Scot might say "Rrroberrrt Burrrns". Video:
http://www. youtube.com/watch?v=F1YZG4jmdLo&t=5m59s (take out the space between www. and youtube, and paste it into your browser. I have to this because otherwise it will try to display it as an embedded video, and it will forget the time. I doubt you guys want to watch 6 minutes of this stupid girl talking to get to the example of a trilled r). - Transliterated "R"
Σ σς - "s" as "sense" - Transliterated "S"
Τ τ - an unaspirated t, which, again, you cannot tell from a d. In fact, you may as well pronounce it "d" as in "dog". That's what they do in pinyin. Of course, if you do that it will share sounds with δ, but oh well. - Transliterated "T"
Υ υ - "uuh" as in German "putsch" - Transliterated "U" or "Y"
Φ φ - "p" as in "pack" - Transliterated "PH"
Χ χ - "k" as in "kiss" - alright, this is supposed to be aspirated, but you can't tell the difference. - Transliterated "CH"
Ψ ψ - "ps" as in "upset" - Transliterated "PS"
Ω ω - the "o" in "dog" - Transliterated "O"