How to Catch Rayquaza in Pokémon Ruby And Sapphire

Beat the Elite Four.

Switch your bike at the bicycle shop in Mauville City to get a Mach Bike (if you do not have one).

Fly to Pacifidlog Town.

Go right from the Pokémon Center. Surf until you reach a red-haired swimmer (she is moving). At this point, go up and then left. You will find a cave.

Traverse through the cave to get to Sky Pillar.

Now, enter the tower.

You need the Mach Bike to traverse through the puzzle. Ride over the cracked floors quickly. It is best to figure out the maze beforehand (Internet or experience-wise). On the second floor with cracked tiles, ride to the end of the maze, and let yourself fall through the third to last cracked tile. You'll fall and reach the rock-blocked stairs. This is the only puzzle; the rest is just going up stairs.

Go up the stairs to find Rayquaza at Level 70.