There's two ways to say the date.
You could say:
The grand opening is on June the first.
Or:
The grand opening is on the first of June.
You either say the month first and then the day or the other way around.
It is May the twenty-second today. It is the twenty-second of May today.
British English: DAY/MONTH/YEAR. American English: MONTH/DAY/YEAR