Jewels appear randomly (and very rarely) with kitten boxes when they are made.
However, if you are breeding Fancie Cats (which are the cats you exchange jewels to get) you are guaranteed a jewel with evey kitten box they make. You breed your Fancie Cat with a normal cat, never breed two Fancie Cats together.
You need 10 Diamonds, 20 Rubies and 30 Emeralds to exchange for a Fancie cat. We can now select which Fancie cat we want - the display and vendors are in the front section of the Main Store.
You can read more about Fancie Cats and Jewels here.
You can also buy the jewels on the secondary market.
Eleanor