Cats can often be distrustful at first, so it's best to let them come to you. Don't come on too strong, or you risk scaring your furry friend away.
When you manage to get close to it, put out your hand slowly and don't make any sudden movements that could spook the cat. It's best to start at the areas where its facial glands are located: around the ears, chin, and cheeks.
Once the cat is comfortable with you, you can start stroking down its back. It's best to move slowly and predictably, and to avoid the belly (no matter how tempting) as you'll likely get scratched.
Cats have very distinct body language, and once you learn it, you'll be able to better understand what a cat is thinking and how you should approach it.
A cat that initiates contact with you with its tail upright is one that would respond well to being pet. A relaxed posture and interested facial expression is also a good sign, as it shows they're comfortable and are interested in you. Purring is an especially good sign.
A cat that is turned away from you has no interest in you, and would rather be left alone. If it remains passive with no reciprocation to your affection, has its ears flattened, and thumps or swishes its tail, it's best to walk away and try again later.
When approaching a cat, no matter your level of familiarity, always start slow and watch for cues. Start at the head and run your hand from the top of its head down to the back of its neck. If it leans into your touch or start purring, you know it's alright to keep going.
Keep petting in the same motion, eventually going until you're petting all the way down to its back. Always go with the grain of the fur, not against. Most cats like being stroked and scratched on their head, chin, and behind their ears. Experiment and see what this particular cat likes. Don't get offended if it runs away, cats are fickle creatures and will come back for more pretty soon.
Most cats are friendly and they like to be petted. However, if you wrongly pet a cat, it can make the cat aggressive. Do not pet a cat on the tummy, legs, or tail. If you are meeting the cat for the first time, pet the cat below their chin, around the ears and cheeks, or on the back of their head. If the cat fees shy or dislikes your touch, don’t pet them. Be very gentle and never apply pressure or hit them. If the cat runs away or hides, it’s probably a sign that they are not interested in receiving affection from you or they could be frightened.