Get the animal's attention:
it is imperative that you do not startle the animal
Next, VERY slowly approach the animal, low to the ground, so you intimidate it as little as possible. Get within 10-15 feet of the animal.
Once you are close to the animal, you must let it approach you.
Do NOT look a stray dog in the eyes for more than a second at a time. Dogs consider this to be a sign of domination, and it can cause the dog to think you want to fight.
Hold out your hand so that the back of your hand is facing the animal.
If it doesn't come to you, slowly - very slowly - start to take baby steps toward the animal.
If it's a dog and it snarls and bares its teeth or a cat and it's growling or hissing at you, do not run. Stay calm and slowly back away.
When the animal sniffs your hand, don't move until it's done.
When it is, you can pet your new friend. Start by very slowly moving your hand from the front of its face to just behind one of its ears, and scratching gently.
clipped from: www.wikihow.com