To welcome an animal to its enclosure, you need to collect all its cards first.
If you have the enclosure built, go to the animal collection album and tap the animal's picture. Once you give it a name, the animal will be delivered to its enclosure.
If you don't have the enclosure built yet, go to the Enclosures tab at the Zoo Shop and proceed to build the enclosure. You can only build enclosures if you have at least one card of an animal in that family.
Once you welcome all four animal family members to their enclosure, you'll get Township Cash as a reward.