Since the net is in the middle of the court during play, it makes sense that the ball might make contact with it at some point. If the ball does hit the net and go into the opponent's court, the ball is considered live.
If the ball hits the net and stays on the offensive team's court, it is considered live as long as the team hasn't used all three of its hits.
On serves, the same rule applies. This is called a let serve.
The ball can touch the net, but a player can't. Any time a player touches the net during rally play, it is considered a net violation.
A player can reach over and under the net, but can't make contact.
An attack block involves penetration, this is when a front row player puts his arms up and over the net to make a block.
Players can use the net to set strategically. A trap set is a pass hit close to the net, to set up for an attack. A deep set is a pass hit far from the net, to confuse the defense.