After discovering Team Aqua/Magma blocking the way to Route 123, you have to go to Route 122, where you find Mt. Pyre.
On the first through third floors of Mt. Pyre, if you are playing Sapphire or Emerald, you will encounter Shuppet. In Ruby, you will encounter Duskull. On the fourth through sixth floors, you have a small chance of encountering the other type (Duskull in Sapphire/Emerald, Shuppet in Ruby).
Mt. Pyre 1F
In the first floor of Mt. Pyre, there is an old woman in the northeast corner who gives you a Cleanse Tag.
If you go west, there is an exit to the outside, but first you should go to the door in the middle of the back wall so you can explore the inside of Mt. Pyre.
Mt. Pyre 2F
On this floor, you can battle Pokémaniac Mark. In Ruby and Sapphire, he has a Lairon, and in Emerald, he has a Rhyhorn. Also on this floor, you can battle Young Couple Dez and Luke, who have a Delcatty and a Manectric.
In the southwest corner of this room, you find an Ultra Ball.
If you fall into the hole, you will go back to 1F.
Mt. Pyre 3F
On this floor, you find Psychic Kayla, who in Ruby and Sapphire has a Kadabra. In Emerald, she has Kadabra, Wobuffet, and Natu, and she might do a Double Battle with Pokémon Breeder Gabrielle, who has Skitty, Zigzagoon, Poochyena, Lotad, Seedot, and Taillow. There is also Psychic William, who in Ruby and Sapphire has Ralts and Kirlia. In Emerald, he has two Ralts and a Kirlia, and he might join Gabrielle in a Double Battle.
On the west side of this room, there is a Super Repel.
Mt. Pyre 4F
On this floor, you can battle Black Belt Atsushi, who in Ruby and Sapphire has Makuhita, Machoke, and Hariyama, and in Emerald just has Hariyama.
There is an item in the southwest corner, but you have to fall from above to get it.
Mt. Pyre 5F
On this floor, in Ruby and Sapphire, there is Hex Maniac Tasha, who has Shuppet and Kadabra.
Mt. Pyre 6F
On this floor, you find Hex Maniac Valerie, who has a Sableye. In Emerald, she might join Psychic Cedric in a Double Battle. He has a Wobbuffet.
Go to the bottom half of the room to find TM30 Shadow Ball, a powerful Ghost Type move.
After you get the TM, go to the left and fall into the hole.
Mt. Pyre 5F, part 2
Walk to the right to find a Lax Incense.
Go to the right, and walk onto the bottom hole.
Mt. Pyre 4F, part 2
Go to the left to find a Sea Incense, then fall into the hole.
Continue going downward until you are in the first floor of Mt. Pyre again. Go to the left side of the room and walk downward out the door where the red carpet is.
Mt. Pyre, Outside
Outside, you can encounter Wingull and Vulpix in the grass. In Ruby and Sapphire, you can find Meditite. In Ruby, you can find Duskull, and in Sapphire and Emerald you can find Shuppet.
Go east until you reach some stairs. Go up the stairs and go west. Go down the stairs on the way to find TM48 Skill Swap.
Go northwest and continue going up the mountain. Soon, there will be mist in the air.
After it becomes misty and you see gravestones nearby, go northeast to get a Max Repel. Go west from there and through some grass to reach a lone gravestone. Check on it to get a hidden Max Ether.
Go northwest to find another gravestone by itself. Check on it to find a hidden Ultra Ball.
Go south and then east, then go north up the stairs to reach the next area.
Mt. Pyre, Summit
In this area, you can find Shuppet, Duskull, and Chimecho (rare).
To the north, you find a Team Aqua/Magma grunt. Make sure that you are a couple of squares away from the grunt when he sees you, because you want to make him walk away from the side. That way, after the battle, you can walk through the path that he was blocking. In Ruby and Sapphire, this grunt has three Zubats. In Emerald, he has Carvanha.
After battling the grunt, walk through the path that he was blocking. The southwest gravestone has a hidden Zinc.
Keep going north up the mountain. In Ruby, the next grunt has Poochyena and Numel. In Sapphire, the grunt has Poochyena and Carvanha. In Emerald, the grunt has Zubat.
Go north again. In Ruby, this grunt has two Numels. In Sapphire, he has two Carvanhas. In Emerald, there are two grunts, one who has a Poochyena and Carvanha, and another who has Wailmer and Zubat. They might team up for a Double Battle.
In the northeast corner, you can find a hidden Rare Candy in the farthest piece of grass.
Go to the very top of the mountain. Archie/Maxie is there, and says that he took an Orb from the top of Mt. Pyre. He and Team Aqua/Magma will leave. The old woman will give you the other Orb (or the Magma Emblem in Emerald). The old man will tell you the tale of the two Legendary Pokémon of Hoenn.
When you are done, you can leave Mt. Pyre.
In Emerald, go to Jagged Pass. You can use the Magma Emblem to open the Magma Hideout in Jagged Pass. Go through the hideout and battle Maxie at the end, then leave the hideout.
Ruby, Sapphire, and Emerald
Go to Slateport City.
In Slateport, you can find Captain Stern outside of a building. Talk to him, and eventually you will see Team Aqua/Magma steal something. They tell you to find them at their hideout in Lilycove City, so go there now.