First off get some info from the web about this animal. It helps so you know what food to get your animal. Then buy all the stuff for your animal. Like a rabbit you may need a brush, cage, food, ect.
When you have your animal at home it may be very shy. It is normal for an animal to be shy at first. Make sure you found and have every thing that "it" will need.
Take it out to help it get used to the environment. It may want to be back where it was put. If an other animal is at home make sure you keep them away from each other. We do not want to cause trouble.
If when they are older and more used to each other you can let them play. It is good for them to play with each other. That way they get there exercise, but still are having fun.
Make sure if you have a small animal you keep it in it's cage and high up if there is another animal at home.
Don't neglect the animal. Pay attention to it and make sure it has the right food and amount of food. If you see something is not right with it, make sure to take it to the vet. Always give it water if necessary.