To do this you will need a few things:
A Stable.
Seed horses. Are the common horses such as the brown,�gray and black mares. It is good to have a lot of them as you will need one each breeding session. And again, they need to be OUTSIDE of your stable. You will use these to set your stable from 0% to ready status.
A special horse or pony. They are the Clydesdale, cream draft, Percheron, Pinto, (brown) pony, pink haired pony, purple hair pony, blue hair pony, Haflinger, Morgan, Mustang, black stallion, Breton etc.

To get started you need to empty your horse stable. There should not be any inside the stable unless for breeding and even then they go back out once the breeding is complete. So, keep all horses outside even for maturing.
What do to:
1. Make sure your stable is completely empty. And that your seed horses are at least 34% ready.
2. Put a seed horse (one that is 34% or higher) in the stable to get the stable ready.
3.Then put in your special horse(s) in the stable. It doesn't matter if the special ones are ready or not.
4. Now put your stallion in the stable. Or find a wandering stallion in your newsfeed. Click on the stable and wait for message to pop up telling you if you received money, xp, farmhands or a foal.
5. If you got a foal then you can post it for your neighbors. Empty the stable and you are ready to start the process again. You can keep doing this until you've used all your common horses. It's even easier if you have your own stallion.
