Like other animals such as humans, cats want to feel safe and free. The more you do to put them at ease and show respect for their autonomy, the better your relationship will be.
With cats, this is extremely easy, because all you have to do is... nothing. They usually don't want much attention, and just leaving them alone demonstrates you're a trustworthy person who isn't going to annoy or hurt them. And yet, this seems to be a very difficult bar for some people to clear; they approach cats with a sense of entitlement to their bodies and touch them when they don't want to be touched. That is not a healthy relationship, regardless of who its between, and it will not endear you to anyone.
Part of the problem is that reading the body language of a creature from another species can be difficult. Much of it has to be learned. It can take a very long time to become proficient at this, but if you pay attention and know what to look for, the broad strokes aren't hard to discern. Cats can be very expressive with their tails. I feel like that gets you 90% of the info you need with most cats.
It also helps to just use some empathy. Would you want to be awoken by the unexpected hand of a stranger? Why are people surprised when this pisses off a cat?
Cats can be very cautious and slow to trust. It could take years before they really trust you and enjoy your company, much less your physical affection. For this reason, stability is particularly valuable in a relationship with a cat; it's sensible to trust someone who's always around and is never a jerk.
Of course, while we can generalize a bit, each cat is their own individual. This is part of why communication can be difficult: you're not just learning a different species, you're learning an invidual member of that species, with their own individual personality and ways of expressing themselves. Certain behaviors are easily recognizable among all cats --- arching their back, spiking up their fur, and hissing is a sure sign of Do Not Want --- but you wouldn't get very far in a human relationship if the only thing you could understand was that screaming means they're unhappy; you'd have to get to know that particular person to learn how to read their body language, how they tend to express their emotions, and what their personality is like. Some cats, like some people, will trust you right away, or even crawl in your lap; some of them want lots of attention, while others want less; some readily speak up and share their emotions, while others are more guarded; some have a playful personality, some are grumps.
It's not a coincidence that the more you treat a cat like a person, the better things will go. Because the world is specist (species-ist), certain decencies that should be extended to everybody are only extended to "people". While some aspects of what is called personhood are human-specific --- anthropomorphization can be misleading --- a lot of it is just about basic moral consideration; a "person" has a special value over and above a non-person. A non-person gets about as much respect as an inanimate object, even if that non-person is alive and looking at you.
Specism is also why talking about the sense of entitlement to petting a cat sounds so much like I'm talking about men's sense of sexual entitlement to women. All forms of oppression have certain features in common. Some men treat women like they're animals; some people treat animals like they're women. Obviously, you should not treat a cat like they're a human man, but you should give them the same respect and see them as much like equal individuals. Consent is key.
Some practical examples:
- If you pick up a cat and they want to be set down... put them down. Wouldn't you freak out if someone grabbed you and wouldn't let you go? How likely would you be to let that person near you again?
- If you're just meeting or having trouble connecting with a cat, get down onto their level. It's less imposing. Think of how you'd feel sitting in a chair with someone big standing over you (who might at any moment grab you and start rubbing you).
- Don't pet a cat if they don't want you to. Let them come to you; let them smell your hand. Don't just approach them and start petting them unless you know them well and that they'll like it. If you're petting a cat, stop if they don't signal for it to continue --- by pushing back, purring, rubbing against you, headbutting, etc. (This known in sexual terms as "enthusiastic consent".)
- If a cat expresses that they want you to stop doing something --- for example, by twitching their tail, growling, hissing, swiping or biting at you --- ...stop doing it. Don't take it as an invitation to assert your dominance. It is not a crime against the social order to respect the boundaries that they set on your interaction, and they won't like you as much if you don't.