Finding a Female Electabuzz
First, you will need to explore the Safari Zone or Route 10 in search of a female Electabuzz. Route 10 is the small patch of grass outside of the Power Plant in the Kanto Region. Walk through the tall grass for a 10 percent chance of meeting an Electabuzz. Exploring the forest section of the Safari Zone will sometimes result in encountering an Electabuzz. Capture the female Electabuzz in a Pokeball.
Suitable Male Pokemon
The Elekid family is of the Humanshape egg group and will only mate with other Pokemon in this family. Although you could use a male Electabuzz, cross breeding with another creature from this group can give the baby Elekid special egg moves such as Ice Punch from a Hitmonchan father or Barrier from a Mr. Mime. As long as the father knows one of these special moves, the Elekid will be born with the egg move.
Breeding Electabuzz
Bring the male Human-Like Pokemon and the female Electabuzz to the Pokemon Day Care Center on Route 34. Enter the house with the red roof on the upper end of the Route and talk to the woman behind the counter. Drop off both Pokemon and go on an adventure. Return to the house after approximately 200 to 300 steps and talk to the man outside to see if your Pokemon made an egg.
Hatching Elekid
Make room for three Pokemon in your party when you go to retrieve your two breeding Pokemon so you can also take the Elekid egg. Pokemon eggs hatch after they are taken on long journeys with you and the other five members of the Pokemon party. The egg becomes one stage closer to hatching after every 256 steps you take. Note that when you read "It's making sounds inside! It's going to hatch soon!" on the egg's status screen, you should get ready to enjoy your new Elekid.