Tim Fitzharris discusses in his book various ways in which to do this. An animals experience with humans will determine your ability to approach and get near them. If the animal lives in a park frequented by humans or in a place where they have grown without fear of humans then your ability to approach them will be easier.
First off you need to know how to find your subject. Where do they usually frequent? Do they hibernate and if so when? Knowing where and when to find your subject will limit frustration. Once you know where and when to find your subject go and track them down.
When you track them down be sure to figure out how your subject feels about your presence and how close it will allow you to get. If the animal becomes agitated back off don't make them feel threatened by you or they may run or fly off on you. If you are standing in their only direction to flee you may get attacked by the frightened creature. So be cautious when approaching any type of wildlife species.
While all wild animals have general characteristics that you should be aware of, every wild animal will also have an individual personality. You will have to figure out your subject's personality on your own when you find them. Look for signs of agitation while approaching your subject and if they appear greatly upset by your presence find a new subject.
Animals hearing is far too keen for humans to sneak up on them. For the most part they will know you're coming. In order to get as close as you want to capture a great picture of a wild animal, you will need to appear non-threatening. Do this by getting low to the ground and crawl if you have to while advancing slowly. Going directly at you subject can work with some animals, but if you have a timid creature you should use a more round about approach.
Another effective method for photographing wildlife is to know where your subject is going to be and get there before them and conceal yourself. Hiding out in a blind allows you to get close to animals without frightening them. There are different methods and types of blinds you can utilize. An automobile makes a good blind because it conceals your body well and is far less intimidating to an animal than your moving body. You want to set up blinds in a spot you know animals will frequent, so again you need to do your homework and know where the best spots are and what time to be there. Blinds don't need to be elaborate they just need to conceal you and allow you close access to your subject, covering yourself and your camera in camouflage is better than nothing.
Another tactic that Tim talks about is bringing the animal to you by baiting. He likes to use peanut butter to draw in his subjects. This seems like an effective method but also seems like cheating to me. Half the fun of taking a good picture is in the reward of capturing an animal by chance, so patience and persistence is the best method for me to capture images of wildlife.