From Bulbapedia, the community-driven Pokémon encyclopedia.
This is the Bulbapedia walkthrough for Pokémon HeartGold and SoulSilver Versions. This walkthrough follows the remade Nintendo DS versions, not Pokémon Gold and Silver.
The guide for those can be found here.
Once you defeat Red on the peak of Mt. Silver, the credits roll for the second time — but the game still isn't done! There are legendary Pokémon to meet and surprising events yet to come.
Your adventure continues as you travel back and forth between Johto and Kanto.
Professor Oak is so impressed with your accomplishments, he offers you the choice of one of the three Kanto starter Pokémon, Bulbasaur, Charmander, and Squirtle. Since you have a team that was capable of defeating Red, you should not have to worry about being defeated in battle. Whichever Pokémon you choose only depends on personal preference. You'll need to have an open slot in your party to accept one, though.
Now that you've acquired a second starter Pokémon, why not look for another? Fly to Saffron City, and make sure that you have an open slot in your party. Enter the Silph Co. building, and you'll run into Steven Stone again near the receptionist by the east wall. He'll ask you a single question: Of a group of stones in front of you, would you choose the green stone, the red stone, or the blue stone? Depending on your answer, he will give you one of the starter Pokémon from his native Hoenn region; Treecko, Torchic, or Mudkip.
Once Steven leaves, follow him back to Pewter City.
Pewter Museum of Science
You'll find him examining one of the exhibits, muttering about the stars in the night sky. Now that you've spoken with him here, you can meet up with him back in Saffron's Silph Co. building again. Speak with him there, and he'll ask to trade your Forretress for his Beldum (and the Dawn Stone that it's holding). Forretress aren't found in the wild, so you'll need to knock a Pineco out of a tree and evolve it first. Beldum are exceedingly rare, so it's a decent trade (though you can find its evolved form Metang in the Safari Zone).
Leave Silph Co, and make your way back into Johto. Your next stop is Mr. Pokémon's house on Route 30.
Mr. Pokémon is all excited, because a friend of his from Hoenn brought him a gift recently. He hands this glittering stone over to you, hoping that you can do more with it than he can. This stone supposedly has some connection to the Embedded Tower, ancient ruins to the west of Cianwood City.
Cianwood City, Cliff Edge Gate, Route 47
Enter the Cliff Edge Gate north of the city, and climb the stairs to the exit. Cross along the cliffs and climb down the ladder inside Cliff Cave to reach sea level. Surf off to the west, and you'll reach a tiny sandbar. Use Rock Climb to scale the first wall and check the rock for a hidden Stardust. Grab the Wave Incense from the southwestern sandbar, and enter the cave to the north.
Near the entrance to the cave, a Hiker tells you about a legend involving the tower. Ages ago, these crumbling ruins formed a tall tower that reached up into the sky, was also embedded in the cliff, and even believed to reach the bottom of the ocean. In short, the ruins used to connect the sky, the land, and the sea to each other. Step inside, and you'll see odd patterns across the floor. In the center of the tower's interior is either Kyogre or Groudon, watching as you approach. Hopefully you've got a decent stock of Ultra Balls! However, like with most other legendary Pokémon, if you do not catch it the first time, defeating the Elite Four and the Champion again will cause each of the super-ancient Pokémon to reappear.
Kyogre's Drizzle ability summons a rainstorm the instant the battle begins. Its Water Spout attack is strong enough to sweep you away, so take care. It can also restore its HP with Aqua Ring. This leviathan is a pure Water-type, so moves like Giga Drain and Thunderbolt will be the most effective. Avoid sending out a Grass-type because of its Ice Beam. Once it is weakened, toss a few Ultra Balls at it and one of Hoenn's super-ancient legendary Pokémon is yours.
Once you catch it, the Hiker appears and explains a bit about the Pokémon. He also tells you that the Embedded Tower was built by the people from Hoenn. Now that you've caught one of the trio, add Kyogre to your team and get back to Pallet Town to show the professor.
Groudon's Drought ability intensifies the sun's rays, which weakens all Water-type attacks. Its Eruption attack is high-powered to begin with, but the intense sunlight increases its destructive force. Like Kyogre's Aqua Ring move, Groudon can use its Rest move to restore its health, as well. Your best chance to catch it is when it's asleep, so take the opportunity to whittle its health down before it wakes up. Once it is weakened, toss a few Ultra Balls at it and one of Hoenn's super-ancient legendary Pokémon is yours.
Once you catch it, the Hiker appears and explains a bit about the Pokémon. He also tells you that the Embedded Tower was built by the people from Hoenn. Now that you've caught one of the trio, add Groudon to your team and get back to Pallet Town to show the professor.
Professor Oak is amazed that you've caught one of the Hoenn trio, but he always thinks of Kyogre and Groudon as a pair—wherever one appears, the other must not be far away. Since you have KyogreHG / GroudonSS with you, he wonders if you could bring them both to him... Unfortunately, Groudon only shows itself to Trainers with shining-silver spirits, while Kyogre only appears to those with golden hearts. This means that you'll need to trade the other one over from the Embedded Tower in the opposite version. If you bring both Pokémon to the professor, he'll reward you with the Jade Orb, which will summon the third member of the Hoenn myth to the Embedded Tower. Only the Pokémon caught inside the tower will work, so you can't bring a different Groudon / Kyogre through Pal Park from the Generation III games and expect the same result.
Rayquaza's Air Lock ability negates all weather-changing moves and abilities. As a Dragon/Flying-type, Rayquaza is extremely vulnerable to Ice attacks, though Rock- and Dragon-type attacks are also super-effective. Look out for its Outrage move, and when it uses Rest, throw as many Ultra Balls as you can. When you show Professor Oak the third member of Hoenn's weather trio, he expresses his fascination that Pokémon have for orbs and stones.