Instructions
Visit Professor Oak in Pallet Town. He will offer you a choice of three Pokemon, Bulbasaur, Squirtle or Charmander. It does not matter which you choose in this case, so choose whichever one you prefer.
Head to the Johto region and make your way to Mr. Pokemon's house, just north of Cherrygrove. Make sure you have the Pokemon that Professor Oak gave you in your party. Talk to Mr. Pokemon and show him the new Pokemon to get the Red Orb item.
Take the Red Orb and make your way to the Embedded Tower on Route 47. To get here, go west from Cianwood City and go through the Cliff's Edge Gate. Come out the other side and you will find yourself in Route 47. Make sure you bring a Pokemon with the move Rock Climb to navigate yourself to the Embedded Tower effectively.
Enter the Embedded Tower. With the Red Orb in your inventory, the legendary Pokemon Groudon will appear in the tower. Save your game before fighting, as this is a one-off battle and your only chance to catch Groudon.
Trade with a "Pokemon HeartGold" user to acquire Kyogre. This Pokemon is available in "HeartGold" as well as previous generation versions but you will need to get the Kyogre that is found in the Embedded Tower in the "HeartGold" version to get the next legendary Pokemon.
Return to Pallet Town in the Kanto region. With both Groudon and Kyogre in your team, head to Professor Oak's lab. Show your new Pokemon to Oak and you will be given the Jade Orb.
Make your way back to Johto and head to the Embedded Tower via Route 47. Rayquaza will now be in the same place where you fought Groudon previously. Take the same precautions as before and save the game before challenging Rayquaza. Weaken the Pokemon and catch it to complete this set of legendary Pokemon.