The modern greeks pronounce the alphabet rather differently from the greek alphabet used in western acedemia, which is based on classical greek. Their pronunciation of the alphabet (alfavet?) and its letters is:

alpha: alfa - a
beta: veeta - v
gamma: ghamma - gh, y, or a soft g
delta: thelta - th, as in 'the'
epsilon: epsilon - e
zeta: zeeta - z
eta: eeta - i
theta: theeta - th, as in 'thought'
iota: yota - i
kappa: kappa - k
lambda: lamtha - l
mu: mee - m
nu: nee - n
xi: ksee - x
omicron: omicron - o
pi: 'pea', not 'pie' - p
rho: roe - r
sigma: sighma - s
tau: taf - t
upsilon: ipsilon - u, or y
phi: fee - f
chi: chee - h, or ch as in 'loch'
psi: psee - ps
omega: ommega - o

For full information on how to pronounce modern greek, see tdent's excellent writeup in Modern Greek pronunciation.