WARNING: THIS ANSWER CONTAINS SPOILERS
The main objective of the Delta Episode it to save Hoenn from destruction that by a meteoroid. I'm going to be giving a walkthrough of the entire Delta Episode because we don't know exactly where you are. Also! Remember to read everything that they are saying, you could get lost if you don't!
After you beat the Elite 4 you will start in your house in Littleroot Town. Your Dad (Norman) gives you two tickets for the Mossdeep Star Show. When you go outside you will meet a girl (Zinnia) disguised as a grunt and setting a new plan, she will introduce herself and the leave. Next, go into your rival's house and your rival will say that a woman came in the house, attacked him/her, stole her keystone and is heading to Petalburg City.
When you get to Petalburg City, you will see Team Magma Admin Courtney/Team Aqua Admin Matt with Wally. They want his Key Stone and your Key Stone. Next they will challenge you to a battle. When you defeat them, they will say that they are going to Meteor Falls for the leader's Key Stone. Wally will thank you but the then says that his Key Stone is missing. You will then get a call on your PokeNav from Steven, asking you to meet him in Rustboro City.
When you get to Rustboro City, go to Devon Corporation. Steven and Mr. Stone will tell you about some bad news. Mr. Stone will tell the story of AZ and the ultimate weapon. He also says that his grandfather, using the story, created infinite energy using similar energy that the ultimate weapon used. Next he tells about the bad news, a huge asteroid, about six miles in diameter, will hit the planet if something is not done about it. He will also mention that Devon Corporation is working on countermeasures but they need the Meteorite Shard from Granite Cave.
When you get to Granite Cave, go to the area with the cave painting of Primal Reversion and Mega Evolution. Zinnia will be looking at the cave painting and says that her ancestors passed down knowledge on how to protect the world. She will then challenge you to a battle, when you win she will give you the Meteorite Shard. Next, Steven will call and tell you to go to Mossdeep City.
When you get to Mossdeep City, go into the Mossdeep Space Center's top floor and hand the Meteorite Shard over to Professor Cozmo. When you do he will explain his plan. Prof. Cozmo needs one more Meteorite Shard, as he asks for you to go get it, Zinnia walks into the room. Zinnia says that going along with Prof. Cozmo's plan will cause history to repeat, she also asks you if you have a better plan. When she leaves Prof. Cozmo will ask you to get the second Meteorite Shard from Meteor Falls, then Steven will leave.
When you get to Meteor Falls go deep into the cave. (You may need some Pokemon with HMs) When you find Steven, he will be with a lady who is a descendant of the Draconids. The lady will say some stuff, then Steven will leave for Rustboro City.
Back at Rustboro City
Go to the Devon Corp. building and you will find a scientist being attacked by a team Magma/ Aqua grunt. When you defeat them he tells you that Team Magma/ Aqua has stolen the Link Cable and that they are heading for Mossdeep Space Center.
Back at Mossdeep City
When you get to Mossdeep City, go to Mossdeep Space Center. When you go inside you will be attacked by FIVE Team Magma/Aqua grunts, they will sent out a horde of Mightenah with Intimidate, so be prepared! After you beat the grunts, go upstairs and you will battle Courtney/Matt along with a grunt. after you beat them, Zinnia will appear and take the Link Cable back, then she will say stuff.
Team Magma/Aqua Hideout
When you get to the hideout, grunts will say that Zinnia is too powerful but luckily their leader is deep in the hideout. After they are done talking, go deep into the hideout to find Maxie & Tabitha/Archie and Shelly battling against Zinnia, Zinnia wins. Zinnia will then say somes stuff. After Zinnia is done saying stuff, Maxie/Archie will give you the Cameruptite (OR)/Sharpedonite (AS). Steven will then call and tell you to go Mossdeep Space Center.
Mossdeep City and Sootopolis City
When you get to Mossdeep Space Center, Steven will suggest you go meet Wallace at the Cave of Origin in Sootopolis City. When you find Wallace at the Cave of Origin talk to him and he will say stuff, he will also tell you to meet him at Route 131.
When you get to Route 131 go to the Sky Pillar. (You will probably need Surf) You will find Wallace there and he will challenge you. When you beat him, he will let you into the Sky Pillar.
When Wallace lets you into the Sky Pillar, you meet Zinnia and Aster there. She then tells you about the history of what happened with Sootopolis City and Rayquaza. Once you reach the top, Zinnia summons Rayquaza. You then fight it and catch it(it's really easy to catch, surprisingly. You'll need to send one of your Pokemon to the PC to make room for Rayquaza). After you catch it, you face Zinnia for the second(and final) time. Her Pokemon are Tyrantrum, Goodra, Noivern, Salamence(Mega) and Altaria. After you defeat Zinnia you fly Mega Rayquaza up into space o.o
This is where you face Deoxys after you destroy the meteorite heading toward Hoenn. You begin your battle against Deoxys with Mega Rayquaza. It is level 80. Catch it or defeat it, you'll receive praise throughout Hoenn. After you come back down from space, you go to the Mossdeep Space Station with May for a bit, then you go back to Littleroot Town. There will also be a scene where Wally tells his father that he's going to the Battle Resort. Then you wake up in bed.