So here's what we have in short: Clean the lens, use less movement, shoot with more light, focus on less details, don't touch the zoom option and find more light again. Then white balance if time allows, target your shot, compose it and finally shoot.
Know that the sophisticated digital cameras are superior to your small built-in camera in all fields, except one, availability and readiness.
And remember, some pictures taken by lousy mobile phone cameras by an amateur with shaking hands have brought thousands of dollars to their authors just because there were no other shots of the events witnessed.
So mind the hints of this article and go out make good pictures.
Good hunting!