Much has been written extensively on street photography, tips, ways to see it and do it and a lot of articles about it.
From my perspective as a photographer located in Cuba and after spending my last years giving workshops on the island, I would highlight the following points.
1.- Don't always be on the move, walking to do street photography is fine, but sometimes finding a good place to wait can cause the image to come to you.
Sometimes it seems that by walking we're trying to find some magical image that always escapes us, it seems as if it is escaping us, sit in a place with good light and possibilities but surely something interesting will appear in front of your camera.
2.- Do not shoot with the same button with which you focus, I know it is probably a new concept but we are many the professional photographers who focus with the AE/AL button. It will take you a few minutes getting used to but in this way, if your position is maintained relative to the photographed object, you do not have to focus every time you shoot and you'll gain speed in your process of taking photos.
3.- Many great street photographers work with fixed 35mm lens and use the hyperfocal distance, so the photo shooting process is much faster because the camera does not have to focus every time we shoot. Try it.
You can check David Allan Harvey website : http://www.davidalanharvey.com/
4.- Try to capture people in unsuspecting attitudes, photographs where everything seems casual have more value than the pictures where you see the photographer, if you were discovered and the situation lost spontaneity you can say goodbye and go back a few seconds later "when no one is waiting for you" or another possibility is to spend enough time in that situation until everyone relaxes and accepts your presence, you will see how the gestures of their faces and their bodies relax.
5.- Sometimes a cigarette (or a bottle of rum) gets better pictures than the best team in the world. I've verified this myself over the years as director of workshops in Cuba that my students tend to be very attentive to their equipment, brands, size, price, etc.
This is certainly an important subject in photography, but I always tell them that offering a cigarette (if you are a smoker) can start a conversation with a stranger and this will lead us to be accepted and to take pictures and make new friends.
6.- In Cuba, the clothes you wear are very important, this rule is easy, try to dress like a normal person, like a Cuban over the street, as you will observe this means escaping from all the tourist clichés. If you can forget your big backpack, your shorts, your explorer hat and start dressing like a person who's living in his own city, this will help you not be the focus of attention.
7.- I propose two options when you find something that interests you, or get increasingly CLOSER or FOLLOW it for longer, we are often too far and other times we see something interesting but do not follow it, do not be shy and if you see something that catches your attention, follow it for a while. To make the picture obvious and keep walking quickly may NOT be the best option.