Report, wait, enter.
A substitute reports to the scorer, identifies the player being replaced and waits near the substitution box. The player enters when recognised or beckoned by an official. Being ready on the sideline is not permission to step onto the court.
A dead ball is not a universal invitation.
Substitutions have specific timing conditions. After a made basket, entry is not normally allowed unless another event makes the ball dead. Free throws, injury, disqualification and certain interruptions have additional rules. The official rule, rather than a blanket “any stoppage” shortcut, determines the opportunity.
Watch the scorer’s table.
A player can stand waiting while several possessions continue. For a viewer, the useful cue is the official’s acknowledgement, not the moment the player removes a warm-up top. Track who leaves as well as who enters to understand the new lineup.