After you Defeat Team Aqua or Magma g o to stoopopolis and steven and the gym leader there will escort u into the cave (note not go in)
To get past the man to enter the Cave of Origin you need to reach a certain point in the story. You will not miss the Cave of Origin as the story directly tells you go there once you've reached that point.
After groudon and kyorgre fight you can go inside the cave
Find the submarine Team Magma stole and defeat themand awaken Groudon
go to dewford and go in the cave the man in there has it
I believe same as Ruby and Sapphire. You cannot reach the cave of origin after the Groundon+Kyogre+Rayquaza+Team Aqua/Magma drama thing because it is blocked by an old man. I tried but i didnt beat the elite four when i did so maybe after the elite four but i doubt it. Steven leads you to the cave of origin so if he hasn't you shoulnt have to go there. The C of O is in the back of Sootopolis
Go to seafloor cavern first. If you're playing with an emulator, there should be maps and stuff that show you where to. Used Youtube, super effective XD
you have to get the ruby and Sapphire rock
To go To The Cave Of Origin You Need To Get The Red Orb You Can Get It In Mt Pyre Once You Go Inside on The First Floor Turn Right You'll Go Into a long Passage Way Go OutsideGo Straight Until You Meet Archie/Maxie Then He Suddenly Leaves For Slateport Once He Does The Man/Woman Will Give You The Red Orb For Safekeeping.
u have to awake raquaza
Anger the ancient Pokemon and cause craziness to happen to the weather.
In Pokemon emerald/Ruby/Sapphire,go to Dewford Town and go to the Cave and ask the man that istanding there and he'll give it to you.
Beat the elite four, receive the national dex, deliver the ruby and sapphire to celio and finally head to four island and go into the house near the pokemart talk to the guy and talk about your hall of fame he will give you a sticker go to mewtwo's cave and the guy will not be there anymore.