Togepi Mystery Egg
The first secret egg you will find in Pokemon HeartGold -- a Togepi egg -- is actually pretty hard to miss if you̵7;re playing through the regular storyline. When you're travelling along Route 30 to Cherrygrove City, take the eastern road and stop by Mr. Pokemon̵7;s house. After a short conversation, he will give you a ̶0;mystery egg.̶1; Soon afterward, in New Bark town, you'll be forced to hand over the egg to Professor Oak for analysis. Continue through the storyline until you reach Violet Gym, where you'll encounter your first three gym battles; the third battle will be against Falkner, the gym leader. Once you beat Falkner, you'll get a call from Professor Elm, telling you that you can pick the egg back up from his aide at the Poke Mart. Travel to the Poke Mart and talk to the aide, and you'll get the mystery egg back. You must walk, with the egg in your inventory, for 2,800 steps before it hatches into a Togepi Pokemon. For a bonus, visit Professor Elm with the hatched Togepi in your lead Pokemon slot, and he'll give you an Everstone.
Arceus Secret Eggs
After you reach the Ruins of Alph, you can unlock one of three secret eggs. However, you must have first obtained an Arceus Pokemon on the "Pokemon Diamond," "Pokemon Pearl" or "Pokemon Platinum" video game. Using a second DS, go to the Union Room of a Pokemon Center on both games, where you can transfer your Arceus over to HeartGold. Once the Arceus is in your party on HeartGold, deposit all of your other Pokemon at the Pokemon Center and head to the Ruins of Alph. As soon as you enter the ruins, a special scene involving your Arceus will begin. You'll be given the option to move on to and select one of three circular symbols, located at each corner of a triangle. Once you select a symbol, a cut scene will ensue in which you'll witness an egg being summoned into existence. The egg will land in your inventory and immediately hatch into one of three Pokemon, depending on the circular symbol you selected. The top symbol gives you a Giratina, the lower left one gives you a Dialga and the lower right symbol gives you a Palkia.
Primo Gift Eggs
In Violet City, a man named Primo can be found standing right next to the town̵7;s Pokemon Center. When you talk to Primo, he asks you your opinion on several subjects; depending on your answer, he'll give you one of several gifts. The potential gifts include eight special box wallpapers and three secret Pokemon eggs: Mareep, Wooper and Slugma. The answers that must be given to receive each egg are different for each player and depend on your five-digit trainer ID number. However, a few websites have tools that list the proper responses for Primo after you input your trainer ID.
Breeding Eggs
Aside from the seven secret eggs in "Pokemon HeartGold," the only way to obtain an egg is to breed one from two existing Pokemon at the Pokemon Day Care, located south of Goldenrod City. You may only breed two Pokemon from the same group type, and they must be male and female. The resulting egg will always be the same breed as the female parent. Ditto Pokemon, which are genderless, may breed with either males or females, as well as with other genderless Pokemon. You must walk a certain amount of steps with each bred egg, depending on the breed, before it will hatch.