This game, as it doesnt feature prominently on Groudon or Kyogre...features on both and Team Magma & Team Aqua's quest to get both of them

Before Leaving Lilycove City, you need to go to Mt. Pyre and get the Magma Symbol. After that you need to go to the Magma Hideout at the base of Mt. Chimney and get through it to the end to met Maxie as he Awakens Groudon
After doing the Aqua Base in Lilycove and the 7th Gym aswell as getting rid of Magma from the Space Center with Steven, you'll need to find the Underwater Cave where Team Aqua are headed. They intend to awaken Kyogre, and they do
Heavy Rain Starts and sometimes cuts out for strong sunlight. Get to Sootopolis City and you will see Groudon & Kyogre are there fighting. However earlier when you left Mossdeep, your rival called you up saying the they had seen a Green Dragon near Pacifidlog town. Steven will let you into the Cave Of Origin to find Wallace. Once you've spoken to Wallace and told him about the Dragon, he'll tell you to meet him at the Sky Pillar
Go to the Sky Pillar and go all the way up and you'll find Rayquaza, Awaken him and he'll fly off. Fly back to Sootopolis and a Cut Scene will Start

Rayquaza Cries out and sends Groudon & Kyogre back to the sea to sleep. Rayquaza then flies off and you'll find him back at the Sky Pillar Catchable
Groudon will be found in the Land Cave after beating the Elite Four
Kyogre will be found in the Sea Cave after beating the Elite Four