Wildlife photography is challenging in any circumstances. To get great images, you have to understand behavior and be observant to predict those key moments—times when all the elements in the frame come together. In a perfect world, the animals will be considerate enough to restrict their movements such that we can frame them up and lock down the camera on a sturdy tripod. That's seldom the case.
A lot of wildlife photographers use gimbal heads, which provide a measure of steadiness while allowing you to move the camera and follow the action. If you don't have a gimbal head, however, you'll probably be handholding, and because you'll be doing it with long lenses, technique is critically important for achieving sharp photos.
Think of your body as a tripod. To keep the camera steady in your hands, start by thinking about your feet. Take a comfortable stance, with your feet slightly wider than shoulder-width apart. Your right foot should be roughly perpendicular to the direction your lens is pointing and your left foot should be slightly to the left and pointing about 5 to 10 degrees to the right. Golfers would call this an open stance. This gives you a very stable base. Cameras are biased to right-handed and right-eye-dominant photographers in the way the shutter button is positioned. Because of that fact, even most lefties take this right-handed stance.
Because a lower center of gravity is inherently more stable, kneeling or even sitting can give you a better foundation than standing up. If you're kneeling, maintain a similar "right leg back, more or less perpendicular to the subject, and left leg forward" position. If there's a convenient rock, go ahead and sit.
Moving up from your legs, keep your back straight and your shoulders relaxed. Your feet, hips and torso should all be parallel. Tension in your shoulders, in particular, tends to promote some camera shake. Bring your arms into your sides, pressing your elbows into your rib cage slightly. Don't squeeze. By pressing your elbows against your ribs, you're really just ensuring that you don't let your arms fly out, which is very unstable.
With your arms in tight to the body, you'll naturally take a proper grip on the camera and lens. You want to cradle both as much as possible. Position your left hand under the lens, with your thumb and forefinger closest to the subject. Grip the camera body such that your index finger rests comfortably on the shutter button and, if possible, have the heel of your hand supporting the body. If you have small hands or a large camera body, or both, don't worry so much about trying to get the right hand under the body. Taking a grip that places your finger on the shutter button is more important because, if you have to reach for the shutter, you'll tend to jerk the camera as you shoot. You can also get a little added stability by pressing the camera against your head as you look through the viewfinder. Don't go crazy, though. Slight pressure is all it takes.
With the proper stance, body position and grip, you'll have a good platform. That's 90% of the battle. To get the last 10%, here are a couple of helpful pro tips. First, when you depress the shutter button, be sure to press straight down. A lot of photographers inadvertently use the index finger as if pulling the trigger on a gun. That creates a jerking motion, which is an absolute sharpness killer. Second, set your camera to multishot mode and shoot in bursts. This is a great technique because the camera naturally steadies out as you press and hold the shutter. Do a test, and you'll see that the first exposure in a sequence has some blur, it's less in the second, and by the third frame, you'll be at maximum sharpness.
One final note: Everyone's minimum handholding speed is different. The rule of thumb of 1/focal length = minimum handholding shutter speed will just get you in the ballpark. Do your own tests to see what your minimums are with all of your lenses, and when it comes to wildlife, take into account that you'll probably be excited in a moment of action and you'll be less steady, so adjust your shutter speed accordingly.