Scout for good locations
If you are shooting in an unfamiliar territory local knowledge will be imperative. A guide who is also a local will take you much closer to your subject then you can ever be on your own. Having said that a little bit of research of your own will never hurt. At the very least you will be able to communicate with your guide better.
Once you spot the animal, try to get into an angle from where you are at the same level as the animal. This is particularly applicable for big cats, and other animals except for giraffes and elephants. Shooting low from the safety of the vehicle will likely give you great images. The money shot is when the animal is looking straight at you. I have found side lit profiles of big cats great too.
This goes without saying, always shoot in continuous or drive mode. That way you will burn up your memory card faster, but at the same time you will get more shots to choose from. Also, always shoot in RAW.
I prefer to compose with AF points. This allows me to compose and fire away the exposures immediately. With the focus and recompose technique you lose a vital second or two and there is always a possibility of image blur. Sometimes, however, the use of the center AF point becomes obligatory. Such as when you are photographing something which has less texture making a focus lock difficult. Most cameras have the center AF point a cross-type one or a dual cross type one and that increases focusing prowess by some degree.
Never ever be satisfied by seeing the images at the back of the camera. Trust nothing unless you see an image in full size on a well calibrated monitor upon return home. If the light is right and everything else is perfect, milk the hell out of the moment and get as many shots as possible. You won’t realize on the spot that many of those shots might be unusable until you see then on a big screen.