Che ore sono? / What time is it?

The 24-hour clock is typically used in Italy, but Italians will have no trouble understanding if time is expressed using the 12-hour clock.

To express an hour of the day the numbers 1-24 and the verb essere are used.
                     Sono le tre                            It is 3am   (03:00)
                     Sono le ventidue                It is 10pm (22:00)

You will have noticed in the above examples that sono (they are) was used instead of è (it is).
Sono is used for all times except one o’clock, noon, and midnight, which use è:

                    È l’una                                   It is one o’clock (01:00)
                    È mezzogiorno                   It is noon/midday
                    È mezzanotte                     It is midnight

This is because when telling time in Italian, you are expressing “how many hours” there currently are. It would be like saying something along the lines of “(the hours) are three” or  “(the hour) is one”, without having to explicitly state the subject (hours).

To express minutes the words e and meno can be used.
                        e (and)                                     adds minutes to the hour
                        meno* (less/minus)             subtracts minutes from the hour

Ex:             Sono le dieci e venti                        It is ten twenty (10:20)
                   Sono le cinque e cinque                It is five o five   (5:05)
                   È l’una e diciotto                               It is one eighteen (1:18)
                   Sono le undici meno dodici          It is twelve minutes to eleven (10:48)
                   Sone le due meno venti                 It is twenty minutes to two (1:40)
                   È l’una meno cinque                       It is five minutes to one (12:55)

*meno is only used when time is approaching the upcoming/future hour.

We can also express chunks of time using the following:
                  un quarto d’ora                                 a quarter of an hour
                  una mezz’ora                                     a half hour
Ex:
                        Sono le sei e un quarto          It is six fifteen (6:15)
                        Sono le tre e mezza/o            It is three thirty (3:30)

A che ora apre il supermercato?             (At) What time does the supermarket open?

The start time or duration of an activity is expressed, similarly to English, with the pronouns da (from) and a (at/to). Remember that the definite article le is always used to tell time, so when both of the above prepositions are used with time, they must be articulated (combined with le).
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Ex:              

Il supermercato apre alle 9:00 
                                      
Il supermercato è aperto dalle 9:00 alle 20:00 
        
Ho una lezione d’italiano oggi dalle 14:00 alle 15:00

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Ieri ho lavorato dalle 6:00 alle 10:00 di mattina*                           

 The supermarket opens at 9am.

The supermarket is open from 9am to 8pm​.
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​I have an Italian lesson today from 
2pm to 3pm.
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​Yesterday I worked from 6:00 to 10:00 in the morning.

*If you use a 12-hour clock or want to emphasize the time of day, the phrases di mattina (in the morning), di pomeriggio (in the afternoon), di sera (in the evening), and di notte (in the night) can be used.