First of all, no matter what you do you are not going to physically turn into an animal, so just drop that idea right now. Shapeshifting is a reality though. It is done through visualization so that you may carry the power and abilities of an animal with you when you need it. Drawing the courage of a lion in the face of adversity is an example where you can draw on the power of an animal spirit in such a way. Shapeshifting is also a way of getting to know an animal better (the old walk a mile in their shoes bit or perhaps in this case it should be paws). Finally shapeshifting allows you to take on animal form while on shamanic journeys or while you visit the astral plane.
To learn to shapeshift you should be in a place where you can meditate, but where there is enough room to move around. You should be dressed comfortably (or undressed comfortably, if that is your preference) so that you may move freely. Relax, close your eyes, call and greet the animal spirit you wish to shapeshift to. Let yourself become that animal in posture, stance, movement and sound. How does this animal see, hear, taste, touch, smell? What is it experiencing? Move as it would move. Become it with all the abandon of a small child. Experience it as long as you wish. When you choose thank the animal spirit that has helped guide you in learning its ways and then return to your human body. Write or draw your experiences if this helps you.
You can do this with as many creatures as you wish, getting comfortable with their different forms and abilities, so that if you are in need of their strengths you need only don them much as you would a mask. In fact masks have been used as a focus to help in the mindshift used in shapechanging and might be something you would like to try.
The ability to shapeshift can be very useful when you are doing shamanic journeying or astral traveling. If you come across a place where there is no way to continue because of a huge chasm you may choose to take on the form of a hawk or if you find a place too small to enter, become a mouse.
You should be careful not to take on any one form for too long. Changes in your abilities will happen with time, not by keeping the abilities of a certain animal with you at all times. Do not learn to depend on a mask to face the world for you might become the mask. Remember your parents asking you, while you had your face contorted into a nasty face, what would you do if your face froze that way? Although you will have the positive aspects of the creature you have chosen to keep on will also grow into the negative ones. It is all well and good to want the courage of a lion, but do you want the arrogance and pride with you at all times as well?