If we disregard the letter χ (chi), the Greek language is not very difficult to pronounce. Even the alphabet is not very difficult, as some letters are very close to our Latin alphabet. And once you got the basics, what a pleasure to read the label of a good bottle of wine to find out the name of the grape!

Uppercase	Lowercase	Name	Phoneme
Α	α	alpha	a
As in "father". Combined letters αυ (alpha-upsilon, upp. ΑΥ) are pronounced "af" or "av".
Β	β	beta	v
The sound "b" does exist but is transcribed with the combined letters μπ (mu-pi, upp. ΜΠ). Example: μπαρ (bar).
Γ	γ	gamma	*
*The letter γ (gamma) is pronounced as an aspired "gh", except before ε (epsilon) and i (iota), where it sounds like y in "year". The "g" sound does exist but is transcribed with the combined letters γκ (gamma-kappa, upp. ΓΚ).
Δ	δ	delta	th
As in "that". The "d" sound does exist but is transcribed with the combined letters ντ (nu-tau, upp. NT). Example: Donald is transcribed Ντόναλντ.
Ε	ε	epsilon	e
As in "get". The sound transcribed in French by "é" (as in "aisle" in English) exists but is transcribed with the combined letters αι (alfa-iota, upp. ΑΙ). The combined letters ευ (epsilon-upsilon, upp. ΕΥ) are pronounced "af" or "av".
Ζ	ζ	zeta	*
Equivalent to our "z", the letter ζ is pronounced like the French "z".
Η	η	eta	i
There are in Greek 6 ways of transcribing the "i" sound (as in "pit"): the letters η (eta), ι (iota), and υ (upsilon), and the combined letters οι (omicron-iota), ει (epsilon-iota), and υι (upsilon-iota).
Θ	θ	thêta	th
As in "think".
Ι	ι	iota	i
Κ	κ	kappa	k
Λ	λ	lambda	l
Μ	μ	mu	m
The letter μ (mu) combined with the letter π (pi) is pronounced "b".
Ν	ν	nu	n
The letter ν (nu) combined with the letter τ (tau) is pronounced "d".
Ξ	ξ	xi	x
Ο	ο	omicron	o
Π	π	pi	p
Ρ	ρ	rho	*
*The letter ρ (rho) is pronounced "r" as in French or German.
Σ	σ	sigma	s
The ς variant is used at the end of words.
Τ	τ	tau	t
Υ	υ	upsilon	i
Φ	φ	phi	f
Χ	χ	chi	*
*The letter χ, before ε (epsilon) and ι (iota), is pronounced as a soft "sh" (as in the German "ich"). Before the other vowels, it is pronounced almost as the Spanish "jota".
Ψ	ψ	psi	ps
Ω	ω	omega	o