Keeping track of many types of animals and their pedigree can be a challenge. It also is really hard to go back and remember the who, what, when after the fact. Creating a genealogy chart and keeping good notes is a great way to keep track of all this information and your herd.
To add a parent to offspring:
Go to the Livestock tab
Create your new animal or select the animal you've already created.
Click on the genealogy tab.
Either register the animals parents by creating new ones or click "Select a Father" or Select a Mother" (or other relative) from the options.
Add the other relatives in the same way.