After following the events of the Delta Episode, you arrive at the Sky Pillar, where the Draconids can summon Rayquaza.
Sky Pillar 1F
Go north and Zinnia will tell you the first part of her tale. After she leaves, go counter-clockwise in this room to reach a ladder in the far north part of the room. Take the Dragon Scale that you find there, then go back down the ladder. Go south to reach the ladder that Zinnia used. Go up.
Sky Pillar 2F
Go west and then south. Zinnia tells you more of her tale. Afterward, go up the ladder.
Sky Pillar 3F
Go east and listen to the next part of Zinnia's story. Then go up the ladder.
Sky Pillar 4F
Go to the north end of this room, then go slightly southwest and look for a Full Restore hidden under the tiles of the floor above you.
Go southwest, and then when the path is blocked, go east. Listen to Zinnia, then go up the ladder.
Sky Pillar 5F
Go east and south to find Zinnia again. Before you follow her, go west from the ladder, then go down the two ladders you find, and go south to get TM64 Explosion.
Then go back up the two ladders and go east, then go up the ladder that Zinnia went up.
Sky Pillar Apex
At the top of Sky Pillar, watch the cut scene. Afterward, save the game. Now is your chance to catch Rayquaza! If you don't have enough pokéballs, or if you need to put different pokémon in your party, you can do that now.
Try using Dusk Balls (available in Fallarbor Town), and if the battle goes for many turns, start using Timer Balls (available in Rustboro City after you talk to the scientist outside of Rusturf Tunnel). Otherwise, use Ultra Balls. You could use your Master Ball if you wish, but you might want to save it for some other time.
After you Catch Rayquaza
After you catch Rayquaza, you will be asked to send one of your pokémon back to your PC Boxes. After that, watch the scene. Then you battle Zinnia.
In this battle, Zinnia has a level 60 Goodra, a level 60 Tyrantrum, a level 60 Altaria, a level 60 Noivern, and a level 62 Salamence that she can Mega Evolve into Mega Salamence.
You will send out Rayquaza first. Just Mega Evolve your Rayquaza and have it use Dragon Pulse on each turn.
After you defeat Zinnia, watch the cut scene. You will get the chance to catch Deoxys. It's OK if you knock Deoxys out, but you will have to defeat the Elite Four and Champion again to get another chance to catch Deoxys.
After you catch or KO Deoxys, there will be a cut scene that ends the Delta Episode.
After that, you'll be in your room in Littleroot. Go downstairs and your Dad gives you the S.S. Ticket. This allows you to go from Slateport or Lilycove to the Battle Resort.
After your Dad heads out, be sure to talk to your Mom to get the Latiasite (in Omega Ruby) or Latiosite (in Alpha Sapphire).
Get a Johto Starter
When you leave your house next time, you'll hear a call for help. Professor Birch is getting chased by a Shroomish. He'll ask you to take a Poké Ball from his bag. You can choose Chikorita, Cyndaquil, or Totodile. After you choose, the pokémon is sent to your PC Box.
Get a Unova Starter
Go back into your house, then leave again. Once more, Professor Birch calls for help. This time, you can choose Snivy, Tepig, or Oshawott. After you choose, the pokémon is sent to your PC Box.