Summarize:

An unfamiliar cat means one that doesn't know you very well, just as a friend or neighbor's cat. Avoid picking up a stray street cat unless it is absolutely necessary (i.e., to get the cat out of danger or transport a sick or injured cat to the vet). If you must pick up a stray or feral cat, be especially careful not to agitate or hurt the cat, and wear gloves if possible. Make sure the cat knows you are there by waking him with a gentle stroke and speaking in a soft voice. Once he's had a little stretch and is comfortable with your presence, then it's okay to pick him up. This short introduction also allows you to assess if the cat is friendly or not. If he starts to hiss and spit, then it is best to use the scruffing method described in Method 3. But if the cat blinks lazily or even starts to purr, then follow the steps below on picking him up. Then, slide your hands further around the cat's chest so that you are gently gripping the cat. Raise the cat until his front legs leave the ground and the cat is standing on his back legs in semi-crouched or half-rearing position. Support the cat's sternum (the breastbone) with this hand, which will help provide enough support to life the cat's body weight as you lift him higher. With the newly freed dominant hand, scoop the cat's bottom up. Now the cat has all four legs off the ground. This will make him feel secure. You do this by folding your arms across your chest, as if you were crossing your arms, but in fact are holding a cat. Keep the cat's bottom (in the dominant hand) against your chest and slide your hand to the opposite side. Make a shallow arc with the non-dominant hand, rotating the cat in a semi-circle with the head moving from the non-dominant side to the dominant side in an arc away from your chest and arriving back near your armpit. If you've done this correctly, the cat's head is to your dominant side and the bottom to the non-dominant side. In addition, the cat's body should be cradled between your forearms, and he is pressed against your chest. This makes the cat feel very secure, and most good-natured cats are happy to be carried like this. As state above, it's really only ideal to carry a cat if you are at home or in another safe environment where the risk of the cat falling and breaking a bone or, alternatively, getting frustrated and scratching you is reduced. If you must carry a cat and move around at the same time, make sure there are no obstructions in your path and maintain a firm but gentle grip on the cat. Be sure as well to move slowly and deliberately. Running with a cat may cause the cat to become fearful, which makes him more likely to struggle. Avoid carrying the cat in your arms in spaces that make him anxious, such as in the vet's office, on the street, or on stairs or ledges. Remember that cats have delicate bones and there is a greater risk of cat injury if you move around while holding your cat, rather than staying in one spot. As in Method 1, place the cat back safely onto the ground by putting him down the opposite way you picked him up; ground his front paws and support his hind legs. He should step out or lightly jump out of your arms without any trouble. Remember to never fight to hold onto a cat that doesn't want to be held. You risk hurting the cat and yourself. Over time, as the cat learns to trust you, chances are that he will become more open to being held.
Never pick up a stray or feral cat. Approach the cat. Slide one hand behind each of the cat's elbows. Gently raise up the cat. Slide your non-dominant hand further under the cat's chest. Hug the cat to your chest. Carry the cat. Put the cat down.