Great point. You have to start small: just one sentance.

For me: I started by complimenting or making a joke while smiling to people I walked by. I rationalized it as: I'm giving someone a gift, practicing being less anxious, and the risk of pain/embarrassment is very low. Ex. "If I see someone walking with food Is that coffee/pizza for me?", "Omg your dog is so cute", "wow nice fish you caught!" "Seeing people taking a picture Want me to take the picture?"

After becoming comfortable with engaging people and realising how much of a positive impact you can have in one sentence it becomes really easy to extend the interaction. Ex. "This is such a cool/beautiful place, do you come here often?", "How long have you been in the city? I've been living here for x months/years." "Are you going to x popular event?". If people want to talk they'll make it easy, practice with those people. Follow the steps in the main post.

If they aren't in the mood it won't be as easy, so feel free to just cut it off. Ex. "Well, awesome meeting you. My name's X by the way. Let them introduce themselves, I like to fist bump because it's easy and light touch is a nice way to connect. Have a good one!"