I've had a FZ15 for about a year and love it. Nikc really gives good advice but I just want to let the camera do the work so I always use auto-focus. I think that your "blurring" problem might be caused by not focusing. First, make sure you are set on spot focus and spot on the subject. Second, use the view finder not the LCD. And third and most important, pause for a quarter second to let the camera focus. Wait for the green light to come on. Once you get used to it it's almost nothing. You can pre-focus on the spot then just click but you'll see that the camera does need time to focus.
To use the Burst mode push the little button on top of the camera behind the shutter button. Mine had three burst modes. You can shoot three, five or ten shot burst's and then keep the best one. It's a great feature.
Good luck with you're camera. I'm no photographer and don't want to be one but I get great shots with it on totally Auto
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