Cat communication is a highly individual thing with most cats preferring indirect methods of communication. A catís disposition and temperament towards humans is highly individual, though most cats that are socialised early in their lives and never abused are very friendly. Unsocialised cats will be very distrustful towards humans and shy away from them.
Cats communicate by means of body language and, to a lesser degree, through vocalisation.
Eyes are of paramount importance in understanding cats and communicating with them. A cat will stare at whatever it considers a threat and will, conversely, consider anyone that stares at the cat a threat. Cats that are continually staring at humans are expressing a negative sentiment towards them. A cat that looks occasionally at a human and than looks away while slowly blinking is trying to say that it considers the human a friend/non threat. To get a cat to like you, look at it briefly, then look 90 degrees away and slowly wink with both eyes. Repeat as necessary. A cat that stares at an object or place and then briefly stares at its owner is trying to get the owner to look where it is looking and do something with that thing or at that place. This may or may not be accompanied by meowing and is usually a matter of the food/water bowl being empty, or needing to be let out. This behavior is also why cats seem to gravitate to the cat-haters of any group. The cat-lovers all stare at the beautiful cat, complimenting it. What would you do if you walked into a room full of hostile strangers? Seek out the one person not threatening you.
Cat pupils also reflect their mood. Dilated pupils indicate aggression or excitement; tiny pupils and wide eyes indicate fear; narrowed or relaxed pupils and half-closed eyes indicate contentment or calmness.
Like horses, cats signal with their ears. If a catís ears are flattened, it is a definite sign of aggressive intent. If, on the other hand, a cat's ears are folded up against its head, it's very afraid. A catís whiskers will be extended out from their face when the cat is inquisitive, but flattened to the sides of its face when it is prepared for battle. An open mouth is a sign of playfulness. If the teeth are prominently showing, then the cat is aggressive. A cat that "bonks" a human with its cheekbones or forehead is giving a friendly greeting and would like to be petted.
The tail of a cat is perhaps the clearest indicator of its mood. A cat usually carries her tail horizontally behind her, with an upward curve to keep it from dragging on the ground. A rising tail is a sign of interest or confidence. A tail raised to vertical and twitching signifies excitement, though a tom will use the same gesture when spraying (i.e. when marking territory with his urine). A half-raised tail is a sign of a so-so mood, and a tail held low signifies the cat is not happy. A twitching tail that is held low or horizontal is a sign of irritation, while a feline tail that is lashing back and forth is a sign of high excitement and/or aggression. A tail held upright with a bend at the tip is a sign of interest.
A cat lounging with his underside showing is relaxed and friendly; by exposing his most vulnerable side, he shows that he trusts you and is not on guard. This is similar to the basic cat defensive position, so look for other clues. If his claws are extended, he is preparing to defend against an attack, but if his claws are in, he probably just wants to play. A cat will arch her back, puff out her fur along her spine and tail, and turn sideways (all designed to make the cat look bigger) when started or scared; she may also growl, hiss, vocalize, lay her ears back, and show her teeth. Such a cat is best left alone.
Cats can vocalise more than a hundred different sounds.
Purring is a vibration of their vocal box with a frequency of 25 to 150 Hz and it shows contentment and relaxation, which will be followed by a kneading and a nap. In rare occasions when the cat is in shock and is attempting to calm itself, it will also purr. These instances can be recognised by the cat bleeding, being bent and/or flattened in ways they normally can't or having a kittenemerging from its business end. In short, either the cat is happy or desperately wishes it was.
Meowing can mean a lot of different things. Usually a catís meow is a call to the owner to pay attention to the cat. Low meows with chirping and purring almost always signify a greeting. Cats will sometimes chirp without a meow or purr when they are very interested in something. Whining meows are a form of protest. Meows of distress can be recognised by their similarity to the wailing of human babies.
Incidentally, adult cats almost never meow at each other. Since kittens will meow at their mothers, it is speculated that perhaps cats meow at humans because they see us as surrogate parents.
Hissing and growling are obviously dire warnings and should be taken as such.
Some cats can imitate other animal's noises, such as barking or the chittering of a squirrel.
A chattering sound means they've seen something they regard as prey, though to reflect a basic form of mimicry. Most often cats do this while observing song birds, and indeed the "chattering" does resemble avian tweeting to some extent.
Some people report having heard cats actually speak. While the "words" are unintelligible, as a foreign language, observers report the cats appear to hold conversations or recite what sounds like a poem or even a prayer. The Oh Long Johnson cat is addressing another cat. He has his ears back flat and is probably uttering threats.
Cats are getting a bad reputation in large part due to humans not understanding their preferences or not knowing their peeves.
Cats knead. That is, they push their paws repeatedly into a surface, claws in or out, when they are happy, sleepy, feeling frisky, showing affection, marking their territory or all of the above. This is not an act of aggresion on their part, regardless of the consequences of them being in your lap at the time. Any disturbance on your part during this "ritual" of theirs will be met with surprise or irritation from the cat.
Cats are distrustful of strange humans and will avoid being cornered or herded, and you should never attempt to capture a cat, as they will fight you. Leaving a cat its space is always best. Cats require a part of their day on their own, without any interference. Cats will typically only let their humans pick them up, but some breeds, like the Turkish Van or the Bengal, will never consent to being carried.
Stereotypically, Cats Hate Water. Like most blanket statements, there are exceptions; various breeds and moggies have greater or lesser affinities with water (Turkish Vans are famous for swimming), and of course individual personalities vary as well. More stereotypically, cats don't like being wettened without their consent, but then how many humans do you know who enjoy being soaked without warning?
A misconception is that this is bound to always remain true. Regular ambient or slightly warm baths can and will make the cat realize that their owner means no harm in this. Some grows so fond of this that they won't mind temperature AT ALL. Hairless cats need to be bathed regularly anyway.
Some cats don't mind their body being wet, but become extremely uncomfortable if their paws get wet.
Another thing folks with cats will have noticed is that cat do spend time in the sink/bathtub (when it's not being used). Cats are attracted to running water because (in the wild) it's generally safer to drink than standing water. They don't necessarily want to get wet though.
Two things are worth remembering in this context: Cats have slightly higher body temperatures than humans, and cats have fur. Water which is comfortable for you will feel cold to a cat, and wet fur will feel cold the same way wet clothes will for the several hours it takes for it to dry completely. Slightly warmer water and careful drying will help getting your cat into the bath.