Instructions
Visit the Day Care center found halfway on Route 34. Route 34 is situated south of Goldenrod City and north of Ilex Forest.
Enter the Day Care center and hand over Ditto and the Pokemon needed to make an egg. The Pokemon you give to the Day Care with Ditto will create an egg containing an unevolved Pokemon of its species. For example, if you give the Day Care Ditto and a Butterfree, the egg you receive will contain a Caterpie.
Leave the Day Care and continue on your adventure. Return to the Day Care after taking approximately 250 steps to see if the pair of Pokemon have successfully made an egg. The person working at the Day Care will happily give you the egg if you have an open slot in your party of Pokemon.
Walk with the egg in your party, and it will hatch after you have taken a predetermined amount of steps. This number depends on the species inside the egg.