Because speed is an element in street photography, you might be more successful shooting on a day when the weather isn't changing its mind every three seconds. If it's a nice sunny day, set your exposure and don't think about it at all after that. The next thing to think about is focus. If you have auto focus, then it will take care of that for you, but you might want to try manual or even zone focus. I'm just getting used to zone focus myself, but essentially it means you are taking pictures of things that are a certain distance away, and your camera is already set to focus on things that are that same certain distance away. Sometimes you'll get the focus on your subject and sometimes it will be a bit off, but the trick is to just keep shooting. And with street photos, sometimes 'close enough' is still good
If you use auto exposure settings and want to try the zone focus method, you can set the camera to aperture priority at...if I remember correctly, it's f11 or f8. It will give good clarity and good depth of field so the area that will be in focus will be larger. So, say everything between 5 and 15 meters is in focus with those settings and something is happening 7 meters away, then you can just worry about framing the picture without worrying about exposure or focus. Larger apertures will give you less room to play with so your distance judgements have to be much more accurate.
That's the theory, anyway. As I said, I've not had a lot of success with this yet, mostly because I don't practice it that often and also because I'm kind of crap at judging distances. I've been manually focusing for so long that it's pretty much second nature to me, so when I'm out trying to get some street shots, I just make my shutter and aperture settings, leave them where they are, and just frame and focus as quickly as I can.