Team Aqua and Magma
Team Aqua and Magma are like the Team Rocket of the game, however, unlike Ruby and Sapphire where you only face one of them, you face both groups in Emerald. Below is where you'll face them and any other general information.
The first time you'll ever see Team Magma is actually when you're just by the entrance to the chairlift. You'll see two grunts guarding it. If you move onto Meteor Falls you'll find Tabitha, Team Magma's Executive with the Meteorite that Team Magma stole. Head back to the entrance of the chairlift and you'll find that there's nobody there. Take the chairlift up to the top of Mt Chimney. Here you'll find both Team Aqua and Magma battling each other. The path is blocked so you'll have to battle Team Magma. This is also the first time you'll face both Tabitha and Maxie, the Team Magma leader. Once you defeat them, they'll leave with Team Aqua chasing. If you head down Jaggered Path, you'll find another Magma Grunt by a rock acting suspicious. Defeat him and he'll say something about a Hideout.
Team Magma Hideout
The next time you'll hear about them is at Mt Pyre after defeating all of the Team Aqua Grunts. Go to the old lady and she should give you something that she found, a Magma Symbol. Head back to the place you first saw the suspicious looking Magma Grunt. When you get there, the Magma Symbol should react and an opening will appear. Head inside into Team Magma's Hideout. There are plenty of Magma Grunts as well as some very handy items. You'll eventually reach Tabitha. Defeat him and you'll find Maxie with Groudon who is asleep. Maxie will awaken Groudon with something that he stole from Mt Pyre, the Blue Orb. Groudon will awaken but it will flee momentarily. Maxie will blame this on you and challenge you to a battle. After defeating him, Maxie will leave the Hideout and that means you've defeated Team Magma again.
The next time you'll battle Team Magma is at the Mossdeep Space Station after defeating Tate and Liza. There, Team Magma will have invaded the place. If you've visited before and defeated the Gym Leaders, you would've found a letter on the table saying that Team Magma is after the rocket fuel used to launch rockets into space. Defeat all the grunts and make your way to the top floor. There you'll find Steven confronted by Maxie and Tabitha. They'll explain that they're going to blow up Mt Chimney with the rocket fuel. Talk to Steven and he'll asks if you want to battle Team Magma together. Accept and you'll go into a double battle. You should win and once you do, Team Magma will leave defeated once more. After that, you should never have to battle Team Magma again.
Team Aqua actually make their appearance a lot earlier and a lot more often than Team Magma. The first time you'll battle Team Aqua is in Petalburg Forest when a grunt attacks a worker at the Devon Corporation. Defeat the grunt and you'll receive a Great Ball. Head over to Rustboro City and defeat Roxanne. Once you do, you'll see a Team Aqua member running off after stealing something. You'll see a Devon worker chasing him. Talk to him and he'll ask for your help. Go into Rustboro Tunnel and you'll see the Team Aqua member with a Wingull. Just before you enter the tunnel you'll see somebody asking for you to get back something they stole from him. Defeat the Team Aqua grunt and the old man should come in thanking you for saving his Wingull. As you head back to Rustboro City, you'll see the Devon worker that asked for your help before. He'll take you into the Devon Company and up to the president. He'll give you a Exp. Share and a letter for Steven inside Granite Cave. The worker will also ask you to deliver the package to Slateport City's Shipyard. The whole of Devon can now be accessed.
Once you're about to deliver the package to the shipyard in Slateport, you'll see a huge line of Team Aqua members blocking the entrance of the museum. Head north and you'll see more Aqua members blocking the path. Head into the Shipyard and talk to the bald guy. He'll tell you to deliver the package to Captain Stern who is in the museum. Head over to the museum and you'll find that all the Aqua members are inside. Enter the museum and make sure you get TM46, Thief. Head up to the top floor and you'll see Cap. Stern confronted by to Aqua members. Defeat them and Archie, the leader of Team Aqua will come in. He'll have a few words with you before leaving. After this, Cap. Stern will take the package and the route to the north will be clear.
The next time you battle Team Aqua is at the weather station that has been invaded by Team Aqua. Defeat all the Aqua grunts and head up to the top floor. You then battle Shelly, the Aqua Executive. Defeat her and an Aqua grunt will come in, mentioning Team Magma being at Mt. Pyre. Team Aqua will then leave and the professor of the weather institute will give you a Castform holder and a Mystic Water.
Head over to Mt Pyre. Head outside to the mountaintop and you'll see a whole heap of Aqua members. Defeat them and you'll see Archie talking to the old lady. He'll then see you and mention about Team Magma getting the Blue Orb. But he doesn't seem too concerned since he got what he wanted, the Red Orb.
After defeating Team Magma in their Hideout, head to Lilycove and you'll see Team Aqua members around. Head out to the bay and you'll see an Aqua member training Wailmer and blocking your path as well as a strange cave. Head inside and talk to the two people. Then head back out and to Slateport City. Head over to the Harbor where Captain Stern is being interviewed. Talk to him and the interview will end. Then somebody will cry out that they're taking the submarine and there's nothing you can do about it. You'll then see that Archie has taken the submarine. Head back to Lilycove and into the small cave. This is Team Aqua's Hideout. Make your way through the warp tiles and to the end where you'll battle another admin, Matt. Defeat him and you'll see Archie leave with the submarine to somewhere under the sea. Beware that inside the Hideout is the Master Ball. After clearing all of that, all the Wailmer and the Aqua members will be gone.
After obtaining HM08, Dive, head underwater on Route 127. When you reach a small cave, go inside and dive up. This is where Team Aqua have taken the sub. Defeat all the Aqua members and make your way to a foggy cave. At the end you'll see Kyogre. Archie will then come in and battle you. After defeating him, Archie just laughs and tries to awaken Kyogre but like with Maxie and Groudon, Kyogre disappears. At this, Maxie comes charging in with Magma members saying that Archie has made a mistake. He'll take you outside and you'll see that it's very sunny one moment and it's pouring with rain the next. They'll then head off to Sootopolis City to try and stop this. When they leave Steven will then fly over and talk to you before also leaving to Sootopolis. Solve the problem and Maxie and Archie will give up their ambition of capturing Groudon and Kyogre.
Head back to Mt. Pyre after completing the game and you'll see the two returning the Red and Blue Orbs. Maxie will see you but he'll just leave. That is the last of Team Magma and Aqua.