each situtation is different. Many times there's no need to ask permission - just go ahead and take the photo. But it often takes practice to be comfortable doing that.
This question comes up all the time on the streetphoto list:
check the archives (I'll see if I can find a couple of the threads)
Working on it as your own personal project is entirely legitimate - as is saying so: "I'm working on a photo project about Key West...or whatever"