The egg groups:

Amorphous

Bug

Ditto

Dragon

Fairy

Field

Flying

Human-Like

Mineral

Monster

Water 1,2,3

None

Basic Breeding

You can breed two compatible pokemon by figure outing two things

1. They are opposite genders

2. They have the same egg group

Then you put them in the Solaceon Daycare and walk around. The Daycare App is very useful for this.

More Factors of Breeding into newer Pokemon

Ok lets say you breed two Snorlax and you get a Snorlax egg when you wanted a Munchlax egg. You have to give certain pokemon held items to get their lowest form However this only works for baby-staged Pokemon that were discovered after the basic form.

Azumarill + Sea Incense = Azurill

Sudowoodo + Rock Incense = Bonsly

Roserade + Rose Incense = Budew

Chimeco + Pure Incense = Chingling

Blissey + Luck Incense = Happiny

Mantine + Wave Incense = Mantyke

Mr. Mime + Odd Incense = Mime Jr.

Snorlax + Full Incense = Munchlax

Wobbuffet + Lax Incense = Wynaut

Natures If you give the female or Ditto an everstone you will get 50% of getting the holders nature

Egg Moves suggestion by Ty_Gamer of the DDA forums

Certain pokemon can learn certain moves thorough breeding. But only the father is allowed to pass down moves to its off-spring. It will pass any move it has learned from a TM, and any move it knows that id on the off-spring's Egg Move List. However, a father cannot pass down a move that is learned by leveling up unless the mother also knows that move and it is a move that the off-spring could learn naturally from leveling up. For example lets say I wanted a Riolu with Blaze Kick. I'd breed a Female Lucario with a Male Blaziken that knew Blaze Kick. Some times you have to go through breeding chains. Like Ice Punch on Sneasel Male Medicham>Female Lopunny>Buneary/Lopunny with Ice Punch>Male Sneasel/Weavile=Sneasel with Ice punch

Certain Exceptions

Ditto is his name, breeding is his game. He can breed with any pokemon even genderless ones. Like lets say you have a Magnezone and you want another Magnemite, so all you do is breed him with a Ditto. You can use him to breed rare Pokemon such as:

Manaphy

Phione

Rotom

Q&A

Q: I put two compatible pokemon in the Day-care but it says they don't like each other much.

A: It will happen eventually, just be patient

Q: If I breed two shinies will the chance of the egg pokemon be a shiny increase?

A: No, it will be the same.

Q: I put two pokemon of the same type in the day care but no egg.

A: Even if they are the same type doesn't mean its the same egg group.