When my friends told me I won the lottery I leapt for joy, but when I realized it was an April fool, I could have killed them

Quando i miei amici mi hanno detto che avevo vinto alla lotteria ho fatto salti di gioia, ma quando mi sono accorto che era un pesce d'aprile li avrei ammazzati

When in 1940 Orson Welles announced on the radio that the Martians were coming, everybody believed it: it was a remarkable April fools' joke

Un memorabile pesce d'aprile fu quando, nel 1940, Orson Welles annunciò alla radio una fantomatica invasione di Marziani e tutti ci credettero

One of the many theories about the origin of this expression, dates the birth of April Fool's Day back in 1582, when France switched from the Julian calendar (where the new year began around April 1th, according to the Spring equinox) to the Gregorian calendar, which moved the start of the new year to the fixed date of January 1st.
People who didn't realize there had been a change, kept celebrating the start of the new year around April 1st. They were called April fools and became the butt of jokes, one of which was to pin a paper fish on the back of one of them to symbolize an easily caught fish and a gullible person. In France it's called "poisson d'Avril" and in Italy "Pesce d'aprile", still popular.