How to talk to your cat

This may seem like a simple topic, but after studying my own cats I feel that it can be much more complex than what you may think.

But we'll start with the obvious:
An arched back and downward curved tail means your kitty is scared;
Purring means that your kitty is relaxed or happy;
An arrow straight body and tail along with growling or hissing means kitty is angry or feels threatened;
When kitty rubs the side of her face on you, she's claiming her as her own.

The tail gives a lot away about their moods. For instance, a tail that's curved at the end, like a question mark, means she is confused. A tail that's tucked, like a dog, means she is afraid. A straight up-and-down tail means she is happy or content. A twitching tail means she is anxious, excited or annoyed. A tail with crazy hairs sticking up most likely means that kitty is angry or threatened about something.

Just like humans, the eyes are the window to a cat's soul. When a cat slowly blinks while looking at you, consider you kissed by your cat, as it's the same as blowing a kiss.
Wide eyes with dilated pupils are hard to tell, as it could mean she's excited or mad.

Vocally, cats can say a lot more than what you may think. When she has a short, high-pitched meow, she's saying, "hello!"
When she's meowing multiple times in a row, she's excited to see (or talk) to you! Just like humans do when they're excited to see someone, cat's can "chatter" too.
When she's drawing out her meow, she's complaining about something.
If she suddenly meows, kind of like a scream, did you accidentally step on her tail? Could she be fighting with another cat?
A hiss means she's trying to threaten you. Beware.

A cats head gives a lot away about her mood as well. Licking, touching her wet nose to yours or head butting are all signs of affection. When she sniffs your face, she's trying to figure out who you are.
When her ears are pinned back, watch out. She may attack.

Sometimes her mood is easy to read. What do you think my cats are thinking here?

Kneading

If you've ever watched a newborn kitten nurse from its mother, you've seen kneading in action.
Kneading is the action that takes place in which a cat will sit in a crouched position and will push out and retract his claws, alternating between his left and right front paws, while appearing to suck (or nurse) and purr.
Oftentimes, it's done before sleeping and females tend to do this more often whilst in heat.
I hardly see Lily taking part in kneading, but when I do it's normally late at night when she's about to fall asleep. 
Although not all cats will knead the same, it's the same idea. His paws will look like he is kneading dough. However, some of them will leave their claws retracted the whole time, while some may not dig their face into whatever they're kneading in.
There's many variations to kneading, as well as many theories for this behavior. 
One theory says that although it's instinctive for cats while they are babies, as they get older it becomes an act of pleasure or relaxation. 
To help you understand, experts say kneading for a cat is like stretching for a human — and if they happen to take part in this act while sitting in your lap, it's a huge sign of affection.
It has even been said that when a cat kneads on his owner, he is checking to be sure all his owners vital organs are working properly. Although I'm sure cats are unable to actually tell, it just goes to show how much he is saying "I love you" in this action.
It's also been said that this behavior has been passed down from generation to generation, as their ancestors would knead the tall grass to make a bed for them to sleep in. (Kind of like the way a dog walks around in circles before they lay down to go to sleep.)
Another theory says he is releasing his scent onto whatever he's kneading onto just to say — this is mine!
It's also been said it's his way of saying, "I want attention!" It's hard to ignore a kitty pushing her claws in and out of your lap and purring loudly.
I first noticed Charlie kneading when he was just a kitten. 
It was often misunderstood and I thought he was trying to nurse! I punished Charlie by moving him off my lap and pulling his head up. 
Little did I know, he was actually saying he loved me!

Charlie kneading on a blanket. 

You can see how he pushes his face into the blanket and in the beginning, 

you can see how he moves his paws.

Letter from your cat

Dear Human,
Please don't get mad at me if I'm not one to cuddle;
but keep in mind that if something's wrong, I'll be there on the double.
Although I come off this way, I'm not trying to be mean.
Whilst you have a life expectancy of 80 years, I've only got 15.
So when you're upset with me over digging up that plant, spitting up a hairball or knocking something over, keep in mind that I'm just inspecting.
Promise not to be furious if sometimes I get curious.
I'm a cat, what do you expect?
You may not realize it, but you're always on my mind.
While you're out with your best friend, I'm waiting on the return of mine.
Although I'm independent, I still need love, attention and affection.
I may not always want to sit in your lap, as I would rather nap.
But I still enjoy your company and I hope you enjoy mine.
I know I can be pretty grumpy, but you're my favorite person to be around.
Although many think otherwise, I would never plot to kill you.
When I stare at you, I'm observing to make sure everything's okay.
I'm not formulating an evil plan against you and I never would.
Although my claws my say otherwise, my purr should make up for it.
Dog isn't the only "man's best friend," cat is too.

Love,
Your Cat