These lessons in Greek pronunciation were presented by 
Father Anthony Moschonas. And here are his tips:
1)  Try to learn the Greek alphabet.  
Even the best ear cannot render the Greek into English 
without a certain amount of distortion.
2)    Using a dipththong because that is what we see
in English is a BIG mistake.  
For instance, the word

is the transliterated form of the kairos.   What we hear
as 'ai' or ay-ee is simply an 'eh' sound to the Greeks.  
Many apparent dipththongs in English are single sounds 
in Greek.
    3)    The accent on kairos is on the last syllable: keh-ROS.  
There is a slight rolling of the 'r', so make that: keh-RROS.  I
adopted the tactic of placing accented syllables in CAPITAL 
LETTERS, because this is the most graphic way to make the 
difference visible.
    4)    Another important thing to remember is that the 
delta letter is often pronounced as voiced 'th' sound.
I will be designating this in my phonetic column by 
marking the delta sound TH.  
Thus the word paideia will be phonetically rendered as 
    Here is a chart of 29 words from rhetoric, using the 
standard English spelling, phonetic rendering, and Greek 
                  ENGLISH                     PHONETIC                        GREEK
Isocrates Ee-soc-RAHT-es Isokrates
Protagoras  Prot-ah-GOR-as Protagoras
Gorgias (zh)Yur-(zh)YEE-as Gorgias
Aristotle (-es) Air-is-to-TEL-is Aristotles
Diogenes THe-o-(ZH)YEN-is Diogenes
Crates KRAHT-es Krates
Hipparchia Ee-parkh-EE-ah Hpparcha
Aspasia Ahs-pass-EE-ah Aspasia
enthymeme en-thee-MEE-mee enqhmeme
episteme eh-pis-TEE-mee episteme
pisteis PEES-tis pisteis
dianoia thee-AHN-ee-ah dianoia
exigesis eks-EE-(zh)yee-sis exugesis
kairos keh-RROS kairos
eide eY-deh eide
theoros thee-o-RROS qeoros
techne TEKH-neh tecne
nous nus nous
apatheia a-PATH-ee-ah apaqeia
eudaimonia ev-them-o-NEE-ah evdaimonia
dialektike thee-ah-lekh-tee-KEE qialektikh
energeia en-air-(zh)YEE-ah energeia
paradeigma pa-RAH-dig-mah paradeigma
dynamis THEE-nam-is dunamis
arete ahr-ah-TEE areth
rhetorike rhee-tor-ee-KEE rhtorikh
physis FEE-sis fusis
spoudogeloios spoo-tho-(zh)yel-EE-os spovdogeloios
paideia peh-THEE-ah paideia