Given a grasp of the numbers from 1 to 12 and a few other words, understanding the time in Greek is fairly simple. To say the time, always state the hour first and then the minutes last, in the form of "hour" plus or minus "minutes". Only if the number of minutes is not divisible by five do you need to use the word for "minutes", otherwise just the number will do. So at 10:23 you would say "δέκα καί είκοσι τρείς λεπτά" (ΔΕΚΑ ΚΑΙ ΕΙΚΟΣΙ ΤΡΕΙΣ ΛΕΠΤΑ) but for 10:25 you would just say "δέκα καί είκοσι πέντε" (ΔΕΚΑ ΚΑΙ ΕΙΚΟΣΙ ΠΕΝΤΕ). Also, just as in english you can use the words for quarter and half, but still the Greek way round using hour first and either quarter or half second. So here are the words you need:
 

English	Lower	Upper
What time is it?	τι ώρα είναι;	ΤΙ ΩΡΑ ΕΙΝΑΙ;
before (minus)	παρά	ΠΑΡΑ
and (plus)	καί	ΚΑΙ
quarter	τέταρτο	ΤΕΤΑΡΤΟ
half	μισή	ΜΙΣΗ
the morning	το πρωί	ΤΟ ΠΡΩΙ
the evening	το βράδυ	ΤΟ ΒΡΑΔΥ
the afternoon	το μεσημέρι	ΤΟ ΜΕΣΗΜΕΡΙ
minutes	λεπτά	ΛΕΠΤΑ
seconds	δευτερόλεπτα	ΔΕΥΤΕΡΟΛΕΠΤΑ
almost	σχεδόν	ΣΧΕΔΟΝ
about	περίπου	ΠΕΡΙΠΟΥ
exactly	ακριβώς	ΑΚΡΙΒΩΣ

The morning in Greece can refer to when you get up tothe middle of our afternoon - basically until you go back to sleep for the afternoon nap! The evening is then from after siesta until going back to bed which could be in the small hours of the next day. "το μεσημέρι" (ΤΟ ΜΕΣΗΜΕΡΙ) only really gets used to distinguish afternoon from early hours if it would otherwise be confusing.
So putting all this together, here are examples of the time in Greek:

English	Lower	Upper
1:15pm	μιά καί τέταρτο το πρωί	ΜΙΑ ΚΑΙ ΤΕΤΑΡΤΟ ΤΟ ΠΡΩΙ
2:25am	δύο καί είκοσι πέντε το βράδυ	ΔΥΟ ΚΑΙ ΕΙΚΟΣΙ ΠΕΝΤΕ ΤΟ ΒΡΑΔΥ
6:30pm	έξη καί μισή το βράδυ	ΕΞΗ ΚΑΙ ΜΙΣΗ ΤΟ ΒΡΑΔΥ
9:45am	δέκα παρά τέταρτο το πρωί	ΔΕΚΑ ΠΑΡΑ ΤΕΤΑΡΤΟ ΤΟ ΠΡΩΙ
11:55pm	δώδεκα παρά πέντε το βράδυ	ΔΩΔΕΚΑ ΠΑΡΑ ΠΕΝΤΕ ΤΟ ΒΡΑΔΥ
4:10pm	τέσσερεις καί δέκα το μεσημέρι	ΤΕΣΣΕΡΕΙΣ ΚΑΙ ΔΕΚΑ ΤΟ ΜΕΣΗΜΕΡΙ
2 exactly	δύο ακριβώος	ΔΥΟ ΑΚΡΙΒΩΣ
7 o'clock	εφτά η ώρα	ΕΦΤΑ Η ΩΡΑ
about 5am	περίπου πέντε το πρωί	ΠΕΡΙΠΟΥ ΠΕΝΤΕ ΤΟ ΠΡΩΙ

Notice in the above examples the numbers for one and four take their feminine forms. Three also changes to in the feminine:

English	Lower	Upper
1	μιά	ΜΙΑ
3	τρείς	ΤΡΕΙΣ
4	τέσσερεις	ΤΕΣΣΕΡΕΙΣ

NB On timetables you will see the use of "π.μ." & "π.π." (Π.Μ. & Π.Π.) to mean AM and PM. Be carefull however as it is "π.μ." that equates to AM and "π.π." that equates to PM. The use of these is just the same as in Britain distinguishing between midnight to midday and midday to midnight, rather than the more vague definitions the Greeks have of morning and evening.