A great way to practice composing photos of animals is to go to your local zoo. Zoo animals make interesting subjects and you can always count on a large number of animals to be visible.
That said, going to the zoo with your camera doesn't automatically guarantee amazing pictures. Just like in the wild, you have to take a number of things into account in order to get a quality shot.
Time of Day/Time of Year
The first thing to think about is the activity level of the animals you want to take a picture of during your current time of year and the time of day you need to maximize your photo's interest. Lions laying down sleeping doesn't make for the most interesting of photos, and worse, they may only be partly visible. Big cats especially are more likely to be resting in the heat of a summer day, so consider trying to go see them first thing in the morning when they may be moving around more or at least may be sitting up with open eyes.
And Interesting/Realistic Background
A great challenge to set for yourself is to try and take pictures where the background doesn't give away that you are at the zoo. That isn't to say you should try and pass your pics off as taken in the African Savannah, but at least do what you can to mitigate the look of fencing, concrete, etc. For example, compare the shot below to the gorilla and lion above:
The rhino looks ok, and it was cool to get a shot of it on the move, but the door in the background takes away from the picture. The gorilla was shot from above and has a hill behind him, making it look more natural. Even the rock behind the lion, while noticeably made of concrete, at least gives some appearance of being natural.
By trying to get a shot with a more natural looking background you will be practicing the vital skill of studying your subject's background and making it an important part of the photo. Is there a fence behind your subject? Maybe you can get to a higher angle so the grass is the background, not the fence. Or, can you increase your aperture size and take a shallower shot, thereby getting the background to blur beyond easy recognition? Every professional wildlife photographer will tell you to make sure your background is as interesting as possible, regardless of whether it is blurred or sharp, because this is one of the things that will set your photos apart and take them to the next level. Moving around and getting a better background at the zoo where you have time to think about it can help get you into the habit of doing the same thing when you are out in the field and need to plan ahead or make a quick and decision on what your background will be before you miss the action. This can also get you thinking about finding different perspectives which is helpful for all types of photography.
Picking the Correct Camera Settings
Animals at the zoo could be moving around from shade to sun and back again, they could be deep in shadow while you are in the sun, or they could be sunning themselves in direct sunlight. Each of these scenarios present different challenges and require different camera settings. Use these opportunities to figure out which settings on your camera will give you the sharp photo you are looking for under every condition you can possibly find. Animals in the wild often won't give you as much time to take photo after photo, and if you don't know the correct settings when they are doing something worth photographing then you could miss it entirely.
The hornbill above was backlit and extremely underexposed. So underexposed I could probably claim it was an intentional silhouette. Figuring out how to properly expose for the hornbill and balancing it with overexposing the background is something one could easily come across taking bird pictures in a forest. This is the time you want to figure out how to take this picture so you will know how to do it when it really counts.
You can also use this time to experiment with different techniques, like purposefully blurred motion or getting a silhouette photo (but with a better background than the hornbill).
Practicing these artistic techniques when you have the time to do it and in a place where, if you fail to get what you want, you aren't going to be too bummed out, means you will know what to do and have to guess less when it really matters.
Appreciating Wildlife
So, going to the zoo to practice your wildlife photography can give you a great opportunity to practice your essentials. Not only that, but taking photos of the animals can increase the joy of going to the zoo and even help you appreciate the animals all the more.