Five Island
Five Island, also known as Chrono Island, is where the Rocket Warehouse is located. However, before you start messing with Team Rocket, there's other better things to do. Surf west into the Water Labrynth, and you'll find an old man on land. Talk to him, and he'll give you an Egg that contains Togepi. Next, go east in the Water Labrynth to reach the Resort Gorgeous section. You'll reach another peice of land with some trainers and an empty house. Continue east and you'll reach the Lost Cave.
Lost Cave
This is a confusing cave filled with fog, and exits that never seem to go where you want to go. Follow these wise steps to navigate the cave: Go right, up, down, down, right, left, down, right, and up. After that, you'll reach Lady Selphy, who'll battle you with two lv. 49 Persian. After defeating her, she'll take you to her house, which was the empty house you passed by earlier. Go talk to her when you have the Pokemon she wants to see, and she'll give you a Luxury Ball. For items in the Lost Cave, go back and follow these steps for the items you want (begin at the start):
Lax Incrense - right, down
Max Revive - right, up, down, down, right, right
Rare Candy - right, up, down, down, right, left, down, left
Sea Incense - right, up, down, up
Rocket Warehouse
After taking care of all that, it's time to face Team Rocket. Either fly or walk back to the Pokemon Center, and go south from there. After a while, you'll reach Rocket Warehouse. Go inside, and you'll see that familiar spin maze. Play around with the maze, and as you do, be sure to pick up important items such as TM36 - Sludge Bomb and Up-Grade. You want to reach the Scientist in the upper-right hand corner. Fight him, and he'll give you back the Sapphire. Be sure to press "A" against the box in this room for a Nest Ball. You're finally finished with the Rockets!
Now exit the Rocket Warehouse and surf west. Go up and pick up the PP Up. Now surf east a little to get to Memorial Pillar.
Memorial Pillar
Battle all the people on the strip of land, and surf south a bit more. You'll reach a larger island with a huge stone in the middle and a Metal Coat on the left. The huge rock is the grave of the trainer's Onix, Tectonix. If you leave a Lemonade there, the trainer will give you TM42 - Facade.
Now that everything's taken care of, go to One Island and hand Celio the Sapphire gem. With that, the machine is fixed, and now Pokemon from Ruby, Sapphire, & Emerald can be traded to FireRed and LeafGreen. In addition to that, you'll be able to fight the Elite Four again, and will also be able to catch Mewtwo in the Cerulean Cave in Cerulean City. If you fight the Elite Four again, they'll have stronger Pokemon, and you can do that on your own time. Now, it's time to catch the strongest Pokemom: Mewtwo!