Wildlife photography, like landscape photography, can be very dependant on the time of day, the season, the weather and really so many other factors that we have little control over. There is of course an added complication now, in that we have a moving and unpredictable subject to focus on as well, and the behaviour of the animal(s) and how they react to their environment and sometimes to us can play a huge part in being able to take a good photograph.
Most of the time the animals we are trying to capture will be skittish and nervous of us humans being near them, or watching them, and will react with a 'flight' response if they feel threatened, and off they run/fly/walk etc. so patience is very much a virtue here. You need to find a location where they can behave naturally and normally without being disturbed if at all possible. This often means distance, so it should go without saying that most of the time a long focal length is needed. A 70-200mm or perhaps a 135mm prime should be the minimums, perhaps with an extender like I mentioned for the sports photography blog.
Daylight should be your ideal time to do this sort of photography, as the added ambient light will make it easier to keep the ISO low and shutter speed up, effectively freezing the motion. This makes for the simplest of images and they do often look the best. However for eg birds you may want a little bit of motion blur so if you are able to, and the subject is in your viewfinder for long enough, you can experiment with a lower shutter speed as well to perhaps get a bit of blur in the wings.
Some wildlife photographers these days often use a camouflaged lens sleeve, basically a neoprene covering for long telephoto lenses which can otherwise be a very unnatural colour, especially the big Canon lenses which are a startling white normally. This is all about looking inconspicuous and blending it, in an effort to not disturb or frighten your subject. If you're on safari or something similar, this sort of technique is perhaps less important as your subjects are less likely to be scared of you and more likely to be inquisitive and approach you, maybe to suss out if you would make a good snack. Take a vehicle and be prepared to use it!
What I believe makes a good wildlife photograph is some sort of environmental context, so it helps to have the subject interacting or being a true part of its environment, rather than focus solely on tight crops of the animal on its own. By all means have a variety of both, but the vast majority of award winning images like those you see in magazines all have some sort of environmental inclusion. Fast primes can be great if you have the room to move, so 200mm or 400mm, which with their wider apertures can help to isolate your subject a bit better. Failing that the good ol 70-200mm is a great option too, maybe with a extender, to give some versatility, but of course its use is a bit more limited to situations with good light.
Although this series, and this post, focuses more on the lens choices, the camera too plays an important role. For example both Nikon and Canon have a line of high frame rate full frame and crop factor bodies that are incredibly useful for this sort of discipline. Remember that crop factor bodies will have a built in 'extender' for your lenses, giving you 1.5x or 1.6x (depending on brand) multiplier for the focal length, albeit with a bit of a loss of capability and sharpness in low light etc.
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