Its a good thing to at least try to learn some greek, even if only a few words. Learning modern greek should be sufficient to get you by, however there is a dialect in Cyprus, much like in different parts of the United Kingdom, so some greek words may not be fully understood by Cypriots, but don't let that put you off, if you have a basic understanding of Greek, you will slowly pick up the Cypriot dialect(s). You should first try to learn the Greek alphabet which consists of 24 letters as below;
To help you get started with learning the greek language, including learning your first words and putting sentences together you could try learning Greek online which can be done in your own time and at a pace you are comfortable with. We recommend Surface Languages Free Online Greek Course.
There are also over 300 Government adult training centers throughout Cyprus where you can take a course at evening school to learn 'Greek for foreigners'. These courses are Co-financed by the European Social Fund of the EU, and offered free to UE citizens, which makes them extremely worthwhile if you plan to live in Cyprus.
Private language training schools are also numerous and can be found in every major city. These courses can be more flexible with your time, some offering day or evening classes. The whole course is completed faster than the government courses, so this may be a better option if you need to learn greek fast.