The magician holds up a sheet of newsprint and shows both sides to demonstrate that it is real and not one of those collapsible rubber fake newspaper sheets that you hear about. The magician then proceeds to tear the paper into little pieces. The little pieces are smashed together and then opened as a whole newspaper once again. The restored newspaper is then properly recycled.
There is only one sheet of newspaper, so this effect can be performed with no preparation.
If you hold a sheet of newsprint to your lips and blow on the edge so that it vibrates rapidly, the sound is very much like the sound of a piece of paper ripping. The magician performing torn and restored newspaper makes good use of this fact. When the magician appears to be tearing the paper, in reality the paper is being folded and a tearing noise is being made as described. The illusion is quite uncanny, and it is not uncommon for spectators to really believe that they saw the paper torn to bits.
Even though this method is time-tested and effective, some modern magicians prepare to avoid blowing on the paper for one reason or another. They, instead, have a cell phone in their pocket with a ring tone that sounds like paper being torn. Whenever they "tear" the newspaper, a hidden assistant sends them a text message, triggering the sound effect.
Restoring the paper is then a simple matter of unfolding it. The magician must take care during the unfolding to remember not to make the tearing noise. That would ruin the effect and confuse everyone.
Note: The signed, torn, shredded, tarred, feathered, burned, eaten, and restored newspaper effect uses a slightly different methodology.