As per their website www.cryptokitties.co "CryptoKitties is a game centered around breedable, collectible, and oh-so-adorable creatures we call CryptoKitties! Each cat is one-of-a-kind and 100% owned by you; it cannot be replicated, taken away, or destroyed."
3 main requisites to get started
A computer or laptop: This is the easiest requisite since a lot of people have one, then you will need to have google chrome of Firefox web browser.
Metamask: It is an extension that will allow you to interact with the main CryptoKitties website. Just go to the google store and look for the Metamask extension. You can visit their website for more instructions metamask.io. Without is you will not be able to use the CryptoKitties website. Metamask Will act as a digital wallet to save your cryptocurrency.
Ether: Ether is a form of digital currencies that powers CryptoKitties. This is what you will use to buy your first digital collectible. You can get Ether from places like coinbase.com and then transfer it to your Metamask wallet.
Once you have all these 3 main requisites you are set to go and buy your first adorable creature. Once on the CryotoKitties website just browse through the marketplace for the one you like. Rember you will need to login to the Metamsk extension in order to use the Cryotokitties website. You only need one to get started but you might want to buy 2 and breed them and create new collectibles. Have fun!