Relax...treat the camera as a friend and a tool to describe how you feel about a subject..
Most people respect a photographer and try not to walk in front of the lens, but also be polite to the public..don't give them a dirty look if they abscent mindedly walk out in front of you..
I have seen more then one photographer huff and snort and lower their camera in disgust when someone wanders in front of the lens, only to get in return a worse reaction.
And, of course ask to tromp around on someone's property..you will be surprised at how nice folks are letting you wander around their gardens, etc ..it goes like this, gee if this is nice enough or different enough to take a picture of - it must be special to someone else as well...works every time..you might have to sent them the photo by email..so how much does that cost??
Oh, sometimes they follow you around, but not to check up on you, often to just watch you work..again, great experience...and be prepared to share..if you are just new tell them that, don't BS...
Okay I am going to be a pain, but you mean shooting in public, not shooting "the" public right???..I have taken a few photos of folks from different area/countries etc...ALWAYS ASK..if you don't know the language, just point at the camera and them and smile..I have only been turned down once..and that was in Martinique...perhaps a superstituous thing..who knows..but I respected her wishes, smiled and just walked away...
If it is a candid shot you need, not posed..take the photo and then try to explain them what you did..most time folks will just go okay..they may want to see it and laugh at how fat ugly or whatever they are...but they are okay...and yea of course you really should get a model release form, but that is for later...