Catch Latios and Latias in Pokémon Soul Silver or Heart Gold

Want to catch a Latios or Latias on Pokémon HeartGold or SoulSilver? You can, but it may take a ton of effort.

Steps

If you haven't already, unlock every place you can go in Kanto. Go to Saffron City and talk to Copycat. She will mimic you and ask you if you can get her Poke Doll back.
Go to Vermilion City and go inside the Pokémon building. Talk to the guy sitting on the table in the middle of the screen and he will give you the doll.
If you step out, Steven (the champion of Hoenn) will tell you things. He talks about Latios in SoulSilver and Latias in HeartGold.
Latios (SS)/Latias (HG) will roam on the map. Catch Latios/Latias. A good way to catch Latios/Latias is in Route 4 by Cerulean City.
To catch Latias (HG, but SS right now) or Latios (SS, but HG right now), you need to cheat an item. This was in an event. If you have Action Replay, you can use the code listed in the Things You'll Need section. Get the Enigma Stone from the Pokemart. There is a green man to give it to you.
Go to Pewter City and go to the Mining Museum. Talk to Steven and he will tell you to give the Enigma Stone to the Scientist. The scientist will give Soul Dew.
Go outside and Latias (SS) or Latios (HG) will be there. Then battle the Pokémon!

Have Pokémon with moves that inflict status effects such as Sleep and Paralysis. Status effects will make it easier to catch them.
Save before battling. If you accidentally faint them or run out of Poke Balls, you can restart the game and try again.
Get a ton of Ultra Balls!
They are level 40, so make sure you have Pokémon that are of at least that level.
Get a few Master Balls if you want to cheat.

You might not want to use codes from other people as they could be a code that can erase the game file.
Action Replay might destroy your game.
Latias and Latios might be strong.