Act like you're a cat and do cat things - Cats do not Distinguish Humans as a Different Species from Themselves. Dogs modify their behavior to interact with humans, Cats interact with us like other cats. Keep the Following Things in Mind to Communicate with your Cat Effectively.
Cats only Vocalize to "Talk" to Humans and Kittens - Kittens cannot hear very well, so Cats Communicate with their Kittens through meows, and are otherwise silent, except... when communicating with us humans. They will learn how we react to each meow and make the sound accordingly, so there will be a specific meow for "I'm hungry," a yowl for "stop that," a chitter for "pay attention to me," but each sound will be specific to how YOU respond. That's right... they're training you.
I know you're wondering about purring. It can mean contentment or stress. Pay Attention to their Tail to know more.
Pay Attention to Their Tail - It's a lot to go over, but learn what your cat's tail means. They position it and wag it differently for various emotions.
You Get Bored, so Can They - They have certain needs that arise from instinct and the sort of animal they are and have been. They are Scavengers with us, but Hunters in the wild. The Deadliest cat in the world is smaller than your house cat. Get them something to bring out the hunter. Feather Teasers, and Catnip Kickers are Great for Playing with them, and even using as a reward to train them if you're into that. There are also various toys that are good for keeping them entertained while you're away.
They think you're a cat and will play with and fight you like one - Don’t scare your cat if they do something you don’t like, by clapping or making loud noises. Simply remove them from the situation. If/when they claw or bite you, just stop playing with them say, "No," and walk away, don’t hit or yell at him. You can, however, use a firm tone when saying "No," Cats don't necessarily understand words, but they understand the tone in your voice. They will stop doing the behavior and still trust you. For Extreme Cases you can Put them on their back to show them you are the dominant one.
They Learn to Trust or Fear You - The Slow Blink is a way of showing your cat that you are not a threat. It looks a little like closing your eyes halfway two to three times. Imagine that you are trying to not fall asleep. You complete the close and fully open your eyes again. Do it no more than twice while they're looking at you, and notice that over time they will begin to slow blink back at you, almost as if responding. Their belly is the most vulnerable part of their body and the little predator knows it. If they roll on their back and show you their belly then it means they trust you. It’s called a “social roll.” Remember when I said, "they think you're a cat?" You can do the Belly Roll also to show them you are family/trust them too.
Cats are Very Territorial - Cats have Pheromone Sacs in Their Cheeks. Cats Mark their Territory by Rubbing Against Surfaces, and Specifically Rub their Cheeks on Those Surfaces to Mark them as "Theirs." They like things that are "theirs" so let them mark you (they will rub on your leg) and help them "Mark" you as their territory by gently scratching the cheeks. Keep in mind that, due to how cats view their territory, some cats may not be comfortable sharing a home with other cats, especially if the second cat is added after years of being an only cat.
Be prepared for your girl cat coming on to you and your boy cat peeing on the wal - WHAT?! Only if they're not fixed, then these behaviors are part of their mating. Males will spray the walls with urine to mark the territory and let females in heat know where to find him. Females will stick their tail and butt up in the air and pat their hind legs on the ground and meow at you in... horny meows.
Talk to your cat a lot and Socialize with them. Science shows that they actually love us and even prefer our company to FOOD.