As I'm watching so many great enthusiasts over here at deviant art I think myself that it would be great If I can help You a bit in your own progress. I'm lucky person because my friend is very good animal photographer and he gave me tips in begin so it was like a shortcut which I'm offering to you now in this journal post.

I will try to simplify but still concrete as much as possible. I'm also sorry for my bad english but I'm just lazy student. OK here we go!

#####################################
Perspective
#####################################

Now take good attention - correct perspective is very important!


From above subject
It will almost always look BAD and BORING. That because it will make animal legs short and the plain is also affected and it is how 90% amateur zoo photos looks like. So try to avoid this angle as much as possible. Even prepare to lay on the ground. So dress up with expectation that you will get dirty .. I almost everytime return from the zoo with dirty dress!


From same height as animal
That's the correct and probably universaly best angle for animal photography. If you want make good animal photos - just get low to the same level as animal. If animal runnig down from a hill - it mean that you will also get down and capture him in same plane as his body is. I reccomend You buy a knee protectors for more comfortable crouch. Also if you will buy an optical angle viewfinder (actualy it is possible to get it for about 30 EUR) then you can save yourself from need to lay on the ground. However I got to used lay on ground even if there is many visitors around me. They wonder, making fun from me but nobody from them have such good captures as I have!


From lower angle than subject
Well it's not very good angle but much better than from above. It will make animal legs longer but it can put a little dramatic or non usual view into picture.


Wide lens from close up
Looks weird! It make large muzles and small heads. Try to avoid it if it isn't your creative plan. Every focal lenght lower than 50mm is wide angle!


Try use as long focal lenght as possible
That's correct. Why? Because as long focal lenght You will use as small piece in background you'll get and also better possibility to blur background. So! If you have possibility to step back and zoom little bit more then do it!! That is sometime applicable for glass enclosures as well. Try to find angle which will give you space for longer focal lenght. Of course only if it will be good for actual light condition and background.

#####################################
Composition
#####################################

Try to do not amputate if not necessary
If You can cover whole animal then do it! If you want portrait animal look for what is important. Depents on what you want cover. For me most important eye catchers are eyes then muzzle and then ears - and then eventualy chest with front legs. Very often error is that You cover whole animal but amputate another one in background. Try to avoid it!


Learn composition rules to break it!
Funny heh? Well, You have to learn rules to find your personal way to break it and so make your pictures unique. But without rules you'll never understand why are You doing this or that. Search internet for those rules. There is many good articles on internet.


If you're lazy to learn them
Try atleast to do not put your subject to the center!!


Animal in move
Try to put more space in direction which animal is running. So if he is running from left to right then put animal to left. But remember to don't amputate! So if for example a tiger is running in water and there is cutting and splashing water behind him then You can break this rule and put him to the right to include this splashing water on left. Remeber: photography of movement is defacto a photography of a story. So You usualy have to tell viewer what will come or what is done.

#####################################
Light - yes, think of light!
#####################################

That's very often forgotten fact that You as photographer using light for create picture! Not your camera as many beginers think. Camera is medium but light is your true creative tool not otherwise.


Look what angle light is going from!
I really mean it!! Many animal pictures on DA don't respect light and that's kill its creator effort. Think of it! Animal in front in shadow and hardlighted background or animal butt with overburns and head in black shaddow. That's all is bad. Turn Your head on sky and look where the sun is then check out shadows on the ground. When you check sun then you may look for ideal angle which is usualy about 20-45 degree on side from sunlight direction. Why not more? Because animal body will be too much in shadow! Why not from front? Because animal body will have no shadows. Shadows are important to keep some hints about space and form. You can also photograph from behind to make silhouets or hi-key photos which is hard discipline but hey!- let's go play. Remember sun need to be very low at evening or morning to photograph hi-key or silhouets. Do You know why atumn, spring or winter is better for photography than summer? Because sun is usualy in nice angle to earth. In summer the sun is during noon is just above and that's bad because you'll it will not form animal shape not mention problems with correct exposition. Best time for photography in summer is morning or evening.


Flash
External flash is very good thing. But You have to be sure You know what You're doing. You'll need to learn how to compensate flash to use it as filling flash. It is handy during day when sun light is strong and You get heavy dark shadows. Flash also can put nice sparcles into animal eye. BUT!! Use it only outdoor and never flash to nervous or nocturne animals or even worse babies!!!!!! Most animal babies have very sensitive eyes and you can hurt them! Especialy if you flash indoor. And of course try to learn using your flash correctly so then You can minimize amount of flashes. If you're rich You can get more flashes and use them remotely but it is more hard than it sounds.

#####################################
Typical problems
#####################################

Glass enclosures
Glass enclosures are very bad for photography. Not for visitors but for photography for sure. Fixfocal lens usualy have problem with doubled details and sharper zoom lenses have problem with visible softness. Unfortunately You can do nothing with it. Try to put your lens absolutely on glass (without lens hood) and use your hand to try avoid mirroring light and primary to try be orthogonal to the plain of the glass as much as possible. You can also help yourself with correct dress. Try to wear black dress without marks and titles and use also black hat.


Wired enclosures
Wired enclosure is not that big problem as it seems to be. If you can put your camera just onto wire then it will get blured into bokeh because depth of field effect. Yes it can affect bokeh and contrast in picture but images are overally sharper than taken over glass. BEWARE!!! Always stay that way that you can immediately step out else you can get seriously hurt by animal. Also do not put your fingers thru wire!!!


High humidity
It usualy happen in winter or when you enter a tropical pavilion. Immediately turn your camera off!! Else it can get broken as water condensate on inner electronic. Some especialy professional cameras are resistable but how many of us can afford cammera for thousands and thousands dollars? You can use hot air from glass drier to warm up your camera and lens till fog will dissapear (look thru viewfinder if lens is clear). Then you can turn your camera on. Glass driers become pretty common in modern zoo.


Cold
Winter is very nice season for photography. But if temperature fall down too much capacity of your batteries dramatical drop down. My tip is use chemical warmer which You can put in your pocket along with batteries. It is also very nice for warming hands which are usualy absolutely frozen which hurts not mention slow reaction for pressing shutter.

#####################################
Another tips
#####################################

Make a plan
It's much better to shot only one animal per day. If it's possible go to the zoo more than once to watch your animal to see its habits and then make plan for photography. You'll see their usual favorite places, when they are active and et cetera. Then You can easily plan your unique and high quality captures.


Try to use correct equipment
Easy to say - hard to do. True is that if You want photograph animals you need atleast a (d)SLR cammera (pure optical view finder) with fast autofocus and fast reaction. Somebody can argue that your skill is more important then equipment and he have right but surgeon will not do surgery with blunt tools as well. Autofocus may vary for every camera and every lens. Some cameras are faster and more accurate as well as some lens are slow and noisy and some are fast and quiet. Compact cameras and EVF cameras are bad for this job.


Don't be lazy and don't be scared to get dirty
This all is important for your sucessful photography your true passion and effort.

#####################################

SOOO! That's are some basics. More advanced tips will come as well as more basic tips if I will notice it is missing in this post. Good luck and good light and remember no photo is valuable as animal life and confort so be careful and respect animal privacy!