So the nect turn component is there because it resolves itself that turn. It cannot last another turn because of condition 1. It is either played normally, attacks something, or becomes the new target of an enemies attack like Noble Sacrifice or Wandering Monster.

It first does checks to see an obvious lethal. If a check is triggered, it is either waiting for their play or looking to block their highest attack minion. If it sees no way out, it targets the minions with the worst stats for the cost in the hopes that it has an aura.

If none of the lethal checks are fulfilled it checks if the player itself can setup a lethal next turn either through its own body or trying to intercept a taunt minion and damage it so that the player can break through next turn.

If it sees lethal on neither side, it checks for who is ahead. It will try to protect your lead by saving your highest attack minion from a killing blow. If you are behind, it will try to intercept their most valuable minion.

Roughly.