How do you know that a basketball dribble has completed?

Answer 1

Usually it is when the player has both hands on the ball. After this point has been established, the player can take two steps (or nowadays, with the rule change, basically three steps).

This is why one can argue that spin moves where the player seemingly takes three steps is actually two steps because the dribble is potentially still alive (see Dwyane Wade or LeBron James).