For 5 turns, slower Pokémon will move before faster Pokémon.

Trick Room reverses the order in which Pokémon move for moves with the same priority for 5 turns.
This means that the Pokémon with the lower Speed moves first.
If a Pokémon uses a move with increased priority such as Quick Attack it will still go first but after another Pokémon that has a lower Speed and also uses a +1 priority move.
Trick Room's effect immediately ends if used again while the effect is active.
Effects that affect the order within priority brackets override the effect of Trick Room. Pokémon holding a Full Incense will still go last and Pokémon that activate their Quick Claw will go first. Trick Room has a maximally decreased priority of -7 meaning that it will go after all other moves.
On a technical level, Trick Room only works up until a Pokémon reaches 1809 Speed, after which point it will go first regardless of Trick Room's effect.
This is because Trick Room sets every Pokémon Speed to (10000- actual Speed) modulo 8192