When the ball is live, the game clock and shot clock are ticking. You'll always know when the ball is live since players will be moving on the floor. The ball becomes live when the referee gives a team possession of the ball to put it into play.
There are three ways to put the ball into play that will make it live in basketball:
On a jump ball, one player from each team stands in the center circle as the referee tosses the ball into the air. The ball becomes live once the referee releases the ball.
You can learn more about jump balls here:
On an in-bounds pass, the referee will give the ball to a player on the team with possession. This player stands out of bounds on the sidelines or baselines and passes it to a teammate on the floor. The ball becomes live once the player gets the ball from the referee.
You can learn more about throw-ins here:
On a free throw, the referee gives the foul shooter the ball to shoot. Once the shooter gets the ball, the ball becomes live.
You can learn more about free throws here:
A substitution is when a player on the floor is replaced by another player on the bench. Teams can make unlimited substitutions during a game, but only when the ball is dead.
Turnovers can be categorized as either live or dead ball turnovers. A live ball turnover is when the ball stays in play such as a stolen pass, while a dead ball turnover occurs when the ball must be inbounded like after a travel. Usually live ball turnovers are worse for a team because they can more easily lead to a fast break.