What films are they showing tonight?
DANNO — double 'n', stress on first syllable. Not 'dano'.
Ask a friend or cinema staff informally what is on. Common in everyday conversation about going out. Can also be asked of the poster board at the entrance.
'Danno' comes from 'dare' used in the sense of 'to show/put on'. Italians say 'danno un film' the way English speakers say 'they're showing a film'. It is a very colloquial but standard usage found all over Italy.
Cosa c'è in programmazione questa settimana?
What is on the programme this week?
More formal; typical of cinema websites and listings.
Hai visto cosa proiettano?
Have you seen what they're projecting?
'Proiettare' is the technical verb; sounds slightly more educated.
Qual è il programma del weekend?
What is the weekend programme?
Good for planning ahead.
Italian directors like Paolo Sorrentino, Matteo Garrone and Alice Rohrwacher have strong domestic followings — mentioning their names at a cinema sounds culturally informed.