Instructions
Go to the main-menu of "Pokemon HeartGold" and change your Nintendo Wi-Fi Connection settings. Connect to your wireless router and test your access point. Return to the main menu and select "Mystery Gift."
Download the Enigma Stone to "Pokemon HeartGold" by selecting "Get From Friend," "Get From Wi-Fi" or "Get From Wireless." Choose the first option to get the Enigma Stone from a friend, the second option to get it from a Wi-Fi Event and the last option to get it from a real-life Nintendo Event.
Get the Enigma Stone from the green deliveryman at any Pokemon Mart. Take the key item to the Museum in Pewter City. Speak to the fossil reviver and he will inform you that the stone is the Soul Dew.
Exit the Museum after having a conversation with Steven Stone of Hoenn. You will see a Latios sprite nearby. Save your game and walk up to the Latios. Press the "A" button to engage it in battle.
Switch out your current Pokemon and choose a Bug, Dark, Dragon, Ghost or Ice-type Pokemon to battle with instead. Once the Level 40 Latios is severely weakened, attempt to catch it with an Ultra ball.