The turn queue and Additional Turns
Turn order is a queue that effects can add to. The phases of one turn are in the lesson before this one; here the question is whose turn comes next, and how an extra turn changes that.
The turn queue. Turn order is set when the game begins as a repeating set of players. It fills a looping queue of turns, starting with the First Player's first turn and repeating indefinitely (rule 736). When a turn ends, the next player with a turn queued becomes the Turn Player (rule 317.3). Some effects tell a player to "take a turn after this", like Time Warp. These create a temporary Additional Turn owned by that player, inserted into the queue after the current turn (rule 735). Inserting one does not change the game's turn order: its owner just has the next queued turn, and after it is completed it is removed and the queue carries on with the turns it had before (rule 737). If several Additional Turns are queued, they are added in the order the effects that generated them occurred (rule 738).
Notation. The queue is written [A > B > C > D] for four players, with * marking an Additional Turn. If the First Player plays two Time Warps during their turn, through some means, the queue becomes [A > A* > A* > B > C > D]. Time Warp has no Action or Reaction, so a player can normally play it only in their own Main Phase (rule 316.5.b). How could others take Additional Turns on someone else's turn? Promising Future has each player banish one of the top 5 cards of their deck and play it: if the Fourth Player's Time Warp resolves and then the Second Player's, the queue becomes [A > B* > D* > B > C > D]. The Second Player takes a turn next, then the Fourth Player, then the queue returns to its previous turns. This is separate from the additional turns of the end-of-match procedure in the Tournament Rules, and additional turns do not count toward the round cycle (TR 206.1).
Common mistake. "An Additional Turn skips someone." It does not: it is inserted, and the queue resumes where it was.