''No'' is an answer. ''Non'' is a negation. I.e.: ''Vieni con me al cinema?'' ''NO, mi dispiace ma NON ho soldi''. Hope it's clear ;)

/non/ is used near a verb, to negate its meaning. /no/ is used as a short answer, or to express a choice when preceded by /o/, as in these examples: 1. Vuoi andare al cinema o no? 2. Ti piace stare qui oppure no? Possible /no/ answers: 1. no. 1. non voglio andare al cinema. 2. no. 2. non mi piace stare qui, andiamo via.

No is the opposite of yes Non means "not"