Breeding
Breeding happens when two Pokémon that are compatible are left in the DayCare. After 64 interactions they may produce an Egg.
Breeding mechanics in PokéFarm Q differ slightly from the main Pokémon games. Offspring may belong to the same evolutionary chain as either parent, rather than just the mother. Incense breeding is also nonexistent; a Snorlax can produce Munchlax eggs without holding a Full Incense.
Compatibility
The two Pokémon must be the same species or in the same egg group and must be different genders. Ditto can breed with any other Pokemon that's not Ditto or that cannot breed. Pokemon that are in the "undiscovered egg group are unable to breed. Baby Pokémon cannot breed.