Here's how it works:
1. Deposit two Pokémon of opposite genders: The Day Care Man will only give you an egg if you have two Pokémon of opposite genders in his care. You can leave any two compatible Pokémon with him.
2. Walk around: The more steps you take, the faster the eggs will hatch. You can speed up the process by using a bicycle or running around.
3. Receive an egg: After a certain number of steps, the Day Care Man will give you an egg. You can keep leaving Pokémon with him to get more eggs.
Important things to remember:
* You need to have at least one Pokémon in your party: You can't get an egg if you have an empty party.
* The egg will hatch after a certain number of steps: This number varies depending on the Pokémon that will hatch.
* The egg will hatch into a specific Pokémon: The gender of the parent Pokémon will determine the gender of the offspring.
You can also get eggs from other trainers, though this is rarer. You can get some rare eggs from the Game Corner in Celadon City by trading in Game Corner coins, but these are only available after you defeat the Elite Four.