If you are living or working here it would be helpful to speak some Greek.  English is widely spoken in the tourist resorts and shops, however in the winter and even in the summer you may be using shops and services that holidaymakers will not frequent, therefore English is quite often not understood.  The locals will also appreciate you at least trying to speak it so don't worry about getting words wrong.  Greek lessons are available, look out for adverts in the local newspaper, shop windows and ask other English residents, some will have been here a very long time and speak very good Greek.

A first step is to learn the Greek alphabet. It is an excellent way to start. 
Watch Greek television, adverts are great for getting some simple words.
Films are good as they are quite often in English with Greek sub titles.
Look at the Greek translations on maps and road signs it gives an idea of the sound of the letters.
Refresh your knowledge of English Grammar. If you are serious about learning Greek properly then a good knowledge of grammar will help.  The Greek language has more verbs and tenses than any other language.

A few words of Greek below to get you going:


Α α alfa Η η eeta Ν ν ni Τ τ taf
Β β vita Θ θ thita Ξ ξ xi Υ υ ipsilon
Γ γ gamma Ι ι yiota Ο ο omikron Φ φ fi
Δ δ thelta Κ κ kapa Π π pi Χ χ hi
Ε ε epsilon Λ λ lamtha Ρ ρ ro Ψ ψ psi
Ζ ζ zita Μ μ mi Σ σς sigma Ω ω omega


1 ένα  6 έξι
2 δύο  7 επτά
3 τρία  8 οκτώ
4 τέσσαρα  9 εννέα
5 πέντα  10 δέκα


παρακαλώ  para kalo please  
ευχαριστώ  ef har isto thank you
γεία σας    ya sas hello or goodbye (formal or to more than one person)
γεία σου   ya soo hello or goodbye (informal)
ναι  nay yes
οχι   oki no