There's a big difference between being out on the street and being inside a public place like Wetherspoons. Inside a pub, people have the expectation of privacy and, even though it's perfectly legal to take photos it's down to you to decide whether it's ethical or not. However, if people didn't do it, we wouldn't have so much excellent social documentary on how things change down the ages.
Out on the street, what Sassafras says above is about 90% of it. Almost everybody is wrapped up in what they're thinking and doing, and they're almost always not thinking about you at all. If they look at you, they're not thinking, "I must ask that guy about photography"; they're more likely to be looking unthinkingly, or at most thinking, "Is he thinking of taking a picture of
me?". I said, "almost everybody" because there are other photographers out there and street photographers do notice other photographers and categorise them into other street photographers, pros on a job, people who bought a DSLR because the guy in the shop told them to, and people who might have actually done some research and are serious about their photography, all pretty much unconsciously. Everybody else is thinking about what that *!(£&* called them on Twitter, or whether to go for that pint now or later, or whatever is in their heads at the time.
How well you get on (in terms of how many photos you actually get to take) depends on many factors, but the most important one, IMO, is how 'visible' you are. As I said, people not noticing you is about 90% of it. The other 10% is mostly about not
getting people to notice you. You turn up nervously with a Canon 1D with a big white 70-200 f/2.8 and you might as well walk up to people and wave a flag. Or, you look around you a couple of times then lift your phone up as if to check Google Maps, and press the volume button on your headset to take the shot, and you stay invisible - the lost tourist. But it's not just about which camera you use. Some people can still be invisible even with the 1D and the 70-200. It's about your behaviour.
Most of the time, I can stand at Piccadilly Circus (where the whole world passes by) with my Sony mirrorless (or whatever) all afternoon getting shot after shot of people right next to me, across the street, or somewhere in between, and I'm pretty much invisible. And it's because of the way I feel. If I stand there and look at people and realise that they've got their own stuff going on, and that they're not waiting for a chance to poke me with sharp sticks, I can stay relaxed. I can look around and notice potential subjects and let my eyes slide right past without looking at them for any length of time. I know the settings well enough to have the camera set up with only small adjustments needed, even when I'm shooting full manual. I can lift the camera and roll my finger over the shutter button and bring the camera down again smoothly. And only if I think it's necessary, maybe I shake my head and give the camera a small shake as if something has gone wrong, and point it elsewhere and take a shot as if I'm a beginner having camera problems. Or I could lift my camera up and take the shot and then, keeping the camera up, I look around it as if I've just noticed that my subject is standing in the way of my
actual subject, something behind them; I can then move slightly and shoot past them. But
only if I feel it's necessary because I
really want that shot of them. I rarely need to use this kind of trick, but I mention it to give an idea of what's possible, and how you can get a shot of someone even if they're staring at you.
If at some point your brain starts nagging you about that pint, or what's happening on Twitter, ignore it, stay awake, keep looking around. Watch the light to see where it's coming from, what it's doing to the surfaces around you, how it's reflecting, where the shadows are, and so on. You know, regular photographer stuff.
So far I've left out what is probably the number one rule: don't make eye contact with your subject. Unless they actually approach you, that is. Following that rule, I've only ever been challenged once, and that was back in about 2008 by a woman who thought I'd taken a picture of her. I hadn't. I was taking a long-zoom shot past her of the South Bank in London.
Anyway, enough of my rambling. There are quite a few good videos on YouTube about street photography that are worth looking at if you're serious about shooting more street. There are also a lot that are not worth looking at, so look for words in the title like "Tips" or "Do's and Don'ts". Oh, and if you do get some good shots, post them in the
Capture a stranger street style thread. We'd love to see them.