I would like to book from the twentieth to the twenty-third of August.
'Ventitré' — the accent on the final E signals the stress: 'ven-ti-TRÉ'. Always stress the final -é in compound numbers ending in 3.
Use to state your exact dates clearly when making a booking by phone. Clarity about dates is the most important part of a phone reservation.
'Dal... al...' = 'from... to...' — these contractions of 'da + il' and 'a + il' are the standard way to state a date range. In Italian, dates use ordinal numbers only for the first of the month ('il primo'); all others use cardinal numbers: 'il venti', 'il ventitré'.
Arrivo il dieci e parto il tredici.
I arrive on the tenth and leave on the thirteenth.
States arrival and departure separately
Sono tre notti — dall'uno al quattro giugno.
It is three nights — from the first to the fourth of June.
Adds the night count for clarity
Check-in venerdì, check-out lunedì.
Check-in Friday, check-out Monday.
Uses day names instead of dates
In Italy, it is standard practice for hotels to repeat back your booking details to confirm. If they do not, ask them to — 'Può ripetere i dettagli?' (Can you repeat the details?). Always note the confirmation number (numero di prenotazione) if given one.