While cat's do have their own set of facial expressions, they aren't exactly the same as in humans, and you can tell more about their emotional state through body language. As an example, when we see them with what looks like a smile, rather than meaning happy, it could instead be due to them sniffing particular odors with a scent gland in the top of their mouth. Some smells that cats tend to hate include citrus, pepper, certain soaps and some plants such as lavender and lemon thyme.

Way to Interpret a Happy Kitty

Purring and Meows

Most the time purring does mean that it's a happy kitty, but it has to be read within the context of the situation, like a human that smiles when they're nervous. Cats can also purr to let other felines know they are friendly or when they are frightened or feeling threatened as a means to calm them-self down.

Cats have a one of the [widest range of vocalizations](widest range of vocalizations) among domesticated animals. There are different meanings associated with meows that vary in pitch, length and volume.

• Short meow or mew: Standard greeting. “Hello!”
• Multiple meows or mews: Excited greeting. “Great to see you!”
• Mid-pitch meow: Plea for something. “I’d like to eat.”
• Drawn-out mrrroooow: Demand for something. “Open the door NOW.”
• Low-pitch mrrrooooowww: Complaint of a wrong you have done. “Hey – my bowl is still empty!”
• High-pitch RRRROWW!: Anger or pain. “That’s my TAIL you just stepped on!”

-Source

The Slow Blink

This is one that isn't always known. When your cat looks at you with half closed eyes or gives a slow blink, it is showing trust and affection. You can reciprocate this back to show you feel the same about them.

Tail Signals

A cat's tail can tell you a lot about their current mood. While standing, a non-bristled tail that is relatively straight up means they are in a good, friendly mood. The bigger ones to keep en eye our for are when the tail is held low as a potential sign of aggression, between the legs for submission and especially when bristled up that is associated with being very angry.

Ear Signals

Generally a calm, happy cat will have their ears perked up and facing forward. Sometimes the direction of the ear shows a direction they are paying attention to and isn't necessarily a problem. But a good rule of thumb is that the more the ears are turned backwards, the more aggressive the cat is feeling and the more flattened shows submission or fear. The direction and flatness can be combined to give additional insight.

Rubbing and Headbutting

Cats have scent glands in multiple places including their head, lips, chins and tails. When they rub on your leg or give a friendly headbutt, they are actually marking you with their scent, which they only do to things they consider safe.

Kneading or Making Biscuits

When nursing, kittens knead on the momma-cat to stimulate the flow of milk. Some believe the act of kneading continues "trying to duplicate that happy, protected time in their lives." Some others think that it's a remnant of when ancient, wild cats need to trample down grasses to make a be and lay claim to an area. Regardless of why, kneading is a great indicator of a content cat.

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Image Sources:
Litle Kittens
Meow
Blink
Tail wagging
Cat Tail Chart
Cat Ear Forward
Cat Ear Chart
Headbutt
Kneading