Let's have a go with the basics

Α	α	άλφα = alfa	Άννα	Anne	Like a in father
Β	β	βήτα = veeta	βάρκα	Boat	Like v in Victor
Γ	γ	γάμα = yama	γάτα	Cat	Like y in yes
Δ	δ	δέλτα = thelta	δώρο	Gift	Like th in this
Ε	ε	έψιλον = epselon	εγώ	Me	Like e in bet
Ζ	ζ	ζήτα = zeeta	ζωή	Life	Like z in zebra
Η	η	ήτα = eeta	ήλιος	Sun	Like ee in beet
Θ	θ	θήτα = theeta	θάλασσα	Sea	Like th in think
Ι	ι	γιώτα = yota	Ιστός	Web	Like ee in beet
Κ	κ	κάπα = kapa	καλός	Good	Like c in car
Λ	λ	λάμδα = lamtha*	Λαγός	Rabbit	Like l in lemon
Μ	μ	μι = me	μαμά	Mum	Like m in mother
Ν	ν	νι = nee	Nερό	Water	Like n in no
Ξ	ξ	ξι = xee	ξύλο	Wood	Like x in ax
Ο	ο	όμικρον = omikron	όλος	Whole	Like o in only
Π	π	πι = pee	πάγος	Ice	Like p in poor
Ρ	ρ	ρο = ro	ρολόι	Watch	Like r in rain
Σ	σ,ς**	σίγμα = seyma***	σαπούνι	Soap	Like s in see
Τ	τ	ταυ = taf	τώρα	Now	Like t in top
Υ	υ	ύψιλον = eepselon	ύπνος	(the)Sleep	Like ee in beet
Φ	φ	φι = fee	φωτιά	Fire	Like f in Frank
Χ	χ	χι = hee	χήνα	Goose	Like h in hair
Ψ	ψ	ψι = psee	ψάρι	Fish	Like ps in lips
Ω	ω	ωμέγα = omega	ώρα	Time (12.30)	Like o in only