How a cat communicate with you?

You and your cat might speak different languages, but you can still communicate with each other
Important clues such as the look in your cat's eyes, the tone of her voice, the position of her ears and the motion of her tail can reveal her feelings and intentions. You can learn to read these signals so you’ll get a good idea of what's on your cat's mind.
Vocalizing: Your cat has something to talk about
You'll learn a lot when you can interpret your cat's wide vocabulary of chirps and meows. They'll tell you when it's time to get up (at least in your cat's opinion), when he's feeling affectionate and if he's feeling threatened or is in pain.
"Meow" is an all-purpose word. Your cat may be saying "meow" as a greeting ("Hey, how ya doin'?"), a command ("I want up, I want down, More food now"), an objection ("Touch me at your own risk") or an announcement ("Here's your mouse"). Some people have watched their cats walking around the house meowing to themselves.

Body language: Your cat speaks with his whole body

Does your cat arch her back up to meet your hand when you pet her? This means she's enjoying this contact with you. Does she shrink away under your slightest touch? Save the petting for later: She's not interested right now.
Identify communicative behaviors. Some of a cat’s communication with you is based on how she behaves when she is around you. Certain behaviors have consistent meaning among most cats.
A cat rubbing against you is marking you as his or her property.
A wet nose "kiss" is an affectionate feline gesture in which the cat taps her wet nose to you. This means that she likes and feels comfortable around you.

A cat rubbing his head, flank and tail against a person or animal is showing an act of greeting.
Playful head-butting is a show of friendliness, affection.
Cats will sniff a person’s face to confirm her identity based on the familiarity of the smell.
A cat will rhythmically knead with his or her paws, alternating between the right and left feet, as a sign of happiness, contentment, or playfulness. Kneading is an indication that your cat knows and trusts you.
A cat licking you is showing the ultimate sign of trust. Your cat may consider you to be a part of her family, like a mother cleaning her kittens.
If your cat tries to eat your hair, she may be trying to "groom" you. This means your cat really loves you and trusts you.

Some cats will show they really love you by copying what you do. You can test this by playing “dead” on the floor. The cat may sniff or nudge you, then play dead too.
If your cat bites you with little force, it is a warning for you to leave her alone.