What's the right way of picking up a cat?

In order to pick up a cat correctly, you have to make sure the cat feels safe and comfortable in your presence before you pick it up. After that, you need to approach the cat, give it time to get used to you, and pick it up and hold it against your chest, making your little creature feel safe and secure.

◎ Support cat's body, and back legs, then lift to the chest

Introduce yourself to the cat. It can take time for cats to warm up to you, even cats that you own.
Make sure the cat wants to be picked up. Most cats will be able to give you a definite sign that they don't want to be picked up.

Place one hand under the cat's body, behind its front legs, slow and gently. Place the other hand under the cat's back legs, giving plenty of support to its legs and bottom. Now that you're holding the cat with both hands, just gently lift the cat up, towards your chest.

Know when the cat no longer wants to be held. Once the cat starts shifting around, moving, or even meowing or trying to escape your grasp, it's time to set the cat down. You don't want to hold the cat against its will.

◎ WRONG
Cats are heavy, carrying them like how their mother carry them by holding their neck part are not recommended. Other than that, lifting a cat by holding the front legs, might injure them.