Animal Paradise is a very cute game, and likely intended for the youngest of gamers, but there isn't a whole lot of depth to it. The main goal of the game is to interact with different types of animals, from dogs and cats to young chicks and hamsters, trying to get them to fall in love with you.
For the most part, interactions with the different species involved still follow a basic pattern. You will be able to feed the animals different treats and meals, and will have to choose the correct one based on what the title tells you. You can also take your pet out to walk, allowing you to use the DS's stylus to point to the location on the screen that you want your animal friend to go. It is also possible to bathe and play with your animals using toys.
As you interact using the stylus, the pets will have different reactions based on their current needs. For example, if you try to feed one that is not hungry, it will simply walk off the screen and you will have the opportunity to try other interactions instead. When the animal is responsive, you can interact with it until one of you gets tired, or until it begins to show appreciation and love toward you. As an example, you may start off rubbing a puppy's head and he will first show that he likes it by the way he animates, and will eventually roll over and allow you to rub his belly. As you do find the sweet spots on your animals, you will get visual and audio feedback, and eventually earn a heart that shows your pet loves you.
As you progress, your pets will fill their heart meters, and other animals will be available to interact with. Just remember that you can't forget about your old friends in Animal Paradise, or they will get lonely. You will have to continuously go back and play with each and every pet that you unlock.