I am still learning the camera, but have so far settled into using shutter priority mode and setting the shutter speed to 1/500 of a second in good light. This will not freeze a bird in the middle of fast movement, but seems pretty good at eliminating the effects of minor movements. However, annoyingly, auto ISO is limited to 200 in shutter priority mode, so you will have to "manually" adjust the ISO if the light is poor (as kittykat indicated). If the light is very good, you may be able to increase the shutter speed even more, which will of course stop the action even better.
I just tried the outdoor sports mode Doug suggested, but noticed there was no indication in the viewfinder of what shutter speed is being used, making it of somewhat limited use for these purposes IMO. Not sure if that can be changed. I have not tried burst mode yet.
I think with this camera your best shots are only going to come in good light; at other times you are going to have to resign yourself to some noise by using ISO 800 or higher (in number).
By the way, not to change the topic of this thread, but I cannot find on my camera the "zoom resume" feature, mentioned in the manual, in the menu system. If others are aware, I would appreciate a brief explanation or private message.
Jim