I've been out there, in public places, regularly, shooting people.
I often feel very self conscious, especially as I cannot see if people are actually looking at me. I can see their head is turned my way, but I cannot see their eyes.
As mentioned elsewhere on the forum, people at 'events' are easiest to photograph, as there are always lots of cameras around. People expect cameras.
If I see a 'situation' that is static, and especially when people are not looking my way,* I have time to 'compose' the shot, but often you are very restricted in what you can do.
I haven't used a long lens often, but that makes life a lot easier.
Shooting from the hip, or chest, can bring you right among the people you want to portray. If you don't look at them, most won't look at you, and you are more or less invisible to them. You can start practising this now. I found I often ended up with too much sky or too much pavement.
Shoot wide, so you have a margin of error. (Is this the right expression? But you know what I mean.)
That said, I'm only a beginner, and have the occasional hit, but loads and loads of misses.
* I'll upload two of this type later today. Here I had a tiny bit of leeway as far as composition was concerned, but only a very tiny bit.