After exploring Route 120 and 121 following your victory over Winona, you can follow Team Magma/Aqua to Mt. Pyre.
Enter the Mountain
To reach Mt. Pyre, go south from Route 121 to reach Route 122. From there, you can go south and then east to reach the entrance to the mountain. You can optionally go south from the mountain entrance to reach the east side of Route 123, which is only accessible from here.
Mt. Pyre 1F
Go north from the entrance. To the west, you can battel Poké Maniac Mark, who has a level 36 Lairon.
North of there, you can battle Psychic William, who has a level 35 Staryu and level 35 Grumpig.
West of there, you can battle Hex Maniac Valerie, who has a level 36 Sableye.
Go south of Valerie and talk to the old woman to get a Cleanse Tag.
South of the old woman, there is an Ultra Ball.
Go north to the next floor.
Mt. Pyre 2F
Go east to get a Super Repel.
South of the Super Repel, you can battle Black Belt Atsushi, who has a level 37 Machoke.
Southeast of there, you can battle Fairy Tale Girl Momo, who has a level 35 Jigglypuff.
East of the Fairy Tale Girl, you can have a double battle with Young Couple Dez & Luke, who have a level 36 Delcatty and level 36 Manectric.
Go north to go to the next floor.
Mt. Pyre 3F
To the northeast, you can have a double battle with Mysterious Sisters Elle & Aya, who have a level 36 Girafarig and a level 35 Mawile.
Southwest of there, you can battle Hex Maniac Tasha, who has a level 34 Shuppet and level 34 Xatu.
South of Tasha, you can find a Lax Incense.
Go southeast and you can battle Backpacker Darnell, who has a level 36 Kecleon.
East of the Backpacker, you can get a Sea Incense.
If you want to get all of the items in the interior of Mt. Pyre, go west and then north to the next floor. Otherwise, you can use the south exit in this room to go outside.
Mt. Pyre 4F
If you went upstairs, go north to the middle of the room and get the TM30 Shadow Ball from the altar.
Then check on the sparkling spot in the northeast corner to get Medichamite.
Afterward, go downstairs and use the south exit to go outside.
Mt. Pyre Mountainside
Go east, then up the stairs. Go east from there and go up the next set of stairs.
Go west, then go south down the stairs at the end of the patch of grass, and go east from there to get TM61 Will-O-Wisp.
Go northwest from there and up the stairs, then go all the way east and up the stairs. Go northeast to find a Max Potion.
Go south and down the small set of stairs, then go all the way to the west. Go north and use your Dowsing Machine to find a hidden Ultra Ball on a grave.
Go south and through the grass, then go east and use the Dowsing Machine to find a hidden Max Ether.
Then go west and north through the grass, then go east and then north up the stairs to reach the summit of Mt. Pyre.
Mt. Pyre Summit
Go north and you will have to battle a Team Magma/Aqua Grunt. In Omega Ruby, the Grunt has a level 36 Koffing. In Alpha Sapphire, the Grunt has a level 36 Grimer.
Go north and you will battle another Grunt. In Omega Ruby, the Grunt has a level 35 Numel and a level 35 Mightyena. In Alpha Sapphire the Grunt has a level 33 Carvanha and a level 35 Mightyena.
Before going north, go west and use the Dowsing Machine to find a hidden Zinc on one of the gravestones.
Then go to the eastern area. Check on the sparkle to get a Banettite.
Go back to the middle and go up the stairs. You will battle another grunt. In Omega Ruby, this grunt has a level 34 Mightyena and a level 34 Golbat.
Go north and watch the cut scene. Then you have to battle a Team Magma/Aqua Admin. In Omega Ruby, you will battle Courtney, who has a level 38 Camerupt. In Alpha Sapphire, you will battle Matt, who has a level 38 Sharpedo.
Watch the cut scene after the battle.
Before you leave Mt. Pyre, go down the stairs until you can go east. Use the Dowsing Machine there to find a hidden Rare Candy. Then go into the walled area to the south and use the Dowsing Machine there to find a hidden Dire Hit.
Go all the way west and use the Dowsing Machine in that area to find a hidden Carbos.
Follow Team Magma/Aqua to Slateport
That is all there is to find in Mt. Pyre, so fly to Slateport City to follow Team Magma/Aqua. Go to the harbor to find Captain Stern giving an interview. After the scene, go into the harbor building. Go over to Captain Stern. Watch the scene, then you will have to battle a couple of Grunts. In Alpha Sapphire, the first Grunt has a level 36 Mightyena, and the second Grunt has a level 34 Carvanha and a level 34 Golbat.
After the battles, Captain Stern asks you to help. If you say yes, he'll take you to Lilycove City where Team Magma/Aqua went. Otherwise, you can say no if you want to stay here in Slateport for now.
When you go to Lilycove, go to the northeast of the city and Surf northeast. In Omega Ruby, you will reach the entrance to Team Magma's Hideout. In Alpha Sapphire, you will reach the entrance to Team Aqua's Hideout.