In PWO, Egg Moves are special moves that Pokémon are able to obtain through tutoring from another Pokémon of the opposite gender. Also referred to as "breeding". With the inability to produce Pokémon Eggs, NPCs—Move Breeder Jackii in the Route 5 Daycare and Move Breeder Perry in the Route 34 Daycare—will help out with the tutoring process. All Pokémon are placed into certain Egg Groups which determine the potential "parent(s)" that can teach a certain Egg Move to the Pokémon. There are advanced techniques such as "chain breeding", which allow Pokémon a part of multiple Egg Groups to teach Egg Moves to Pokémon only in one and can only learn the move via breeding.
For this demonstration, let's walk through how we would get the Rapid Spin move from a female Blastoise to a male Tentacruel. The process will require chain breeding, but we must start with first part of the chain. Most Eggs Moves will only require this step.
First, we must identify the Egg Groups and potential parents needed to transfer the Rapid Spin move. Checking on an external website (Serebii), it appears that Tentacool, Tentacruel, Shellder, Cloyster, Kabuto, Kabutops, Anorith, and Armaldo can teach the male Tentacruel. They are all a part of the Water 3 Egg Group.
Fortunately, Kabutops is a part of both Water 1 Group and Water 3 Group. The first step is to teach the male Kabutops Rapid Spin. Always select the Pokémon being taught first, then the parent with the move—which in this case, is Blastoise—second.
If you selected in the proper order, the prompt for the Egg Move should pop-up (as if the Pokémon learned the move via level-up). If by chance, you selected the wrong Egg Move by mistake, you can just select "Do not learn this move" and try again. Kabutops now has Rapid Spin!
The job isn't finished yet. A male Kabutops can not teach a male Tentacruel as they are of the same gender. Therefore, we must teach the female Tentacruel Rapid Spin first.
And finally, we can teach the male Tentacruel Rapid Spin through the female Tentacruel, thus completing the chain breeding process.
Other prompts will occur if the Pokémon does not have any Egg Moves to teach or if the recipient has already learned the Egg Move.
Since Smeargle can learn almost any move by using Sketch, it can teach any Egg Move to Pokémon in the Field Egg Group (the largest Egg Group). Click here to learn more about using Sketch with Smeargle.