You can enable sponsorships for animals when editing or adding an animal.

Website Service: You will need to enable the Sponsorships feature. Click here for more information on how to do this Sponsorship Settings and Options

You can enable a sponsorship for an animal at any time.

Where do I find it?

Go to the animal's detail page from your account page. Select the icon to edit the page, then scroll down to the Sponsorship Options.
Click Animals > Animals List and click the Edit icon next to the animal you want to edit for a sponsorship.
Search for an animal from the left navigation bar in your account menu, then click the Edit icon to edit the page, then scroll down to the Sponsorship Options.