The camera in the phone has image stabilization. This reduces the effect of camera shake when shooting in low light (longer shutter speeds). But it cannot help with motion blur caused by the movement of the subject.
So when shooting fast-moving subjects, like kids or pets or sports, etc., you just need to have a lot of light. This is true even with extremely fancy cameras, but modern DSLRs and MILCs with large sensors and large-aperture lenses will do better than these phone cameras with their tiny sensors.
The other thing you will notice when shooting in low light is that the camera will have to use a higher ISO setting. Simply, this is like turning up the amplifier gain (similar to turning up the volume knob on a stereo). And that results in more noise in the image. Just as turning up the volume on a stereo lets you hear more noise when playing back a tape or record.
Again, a large-sensor camera will do better at this.
So as with any camera, you will always do better when you have more light available.
Try to find ways to hold the camera/phone that will help to steady it. With an eye-level viewfinder (like you have on a DSLR) it is easier to achieve a stable hold on the camera. That is because you have three points of contact between you and the camera.
Your face, your right hand, and your left hand. You pull your elbows in against your body, and hold the camera against your face, and you have a three-point system, like a tripod, which is inherently stable.
With any camera that does not have an eye-level viewfinder, on which you are viewing and composing via a screen, you are forced to hold the camera out away from your body. This is inherently unstable.
So a camera with an eye-level viewfinder is always better for stability.
So cheat! Use whatever is available to rest the camera or your hands against. I'm nearsighted, so I need to take my glasses off to see the screen from close-in, so I sometimes do that just so I can hold the phone closer, with my elbows up against my chest. It's not three points, but it's better than holding my arms way out where I can see the screen with my glasses on.
And a rear-display screen can help in some ways. It forces you to see the image just the way it will be seen as a print, or on someone else's screen. And to me, that is helpful for visualizing composition. It's as if you are looking at the final product as you're choosing your camera position. So experiment as you're composing the shots and try to make a good composition by getting the camera exactly where it needs to be to get the perspective and composition you like. Trial and error is instantaneous when you are viewing the image exactly as it will be.
Move around, and take advantage of the small size of the phone and the position of the lens with respect to the edge of the phone to get it crammed into a corner or up against a surface. Remember that you can always rotate an image later, so don't worry if the shot is sideways or upside down if that makes it possible to get the camera position you really want. It's a benefit that the camera is NOT in the center of the phone.
It's easier to get interesting camera positions with these phones than it is with a large camera.
Further, while we often want the shallow depth of field that a large sensor and large aperture lens can give, because you get good subject isolation, sometimes we wish for deeper depth of field, and these tiny cameras inherently give us that.
This is particularly true when shooting close-ups or macro shots. A tiny camera makes macro shooting much easier than it is with a large-sensor camera. The inherently deep DOF keeps more of the subject in sharp focus. And you can use that characteristic along with the camera being close to an edge of the phone to get interesting point of view with extreme foreground in focus as well as extremely distant objects, too.
Rest the top edge of the phone against a tree or wall, and you get stability and the possibility of a very interesting composition with part of the tree or wall in the shot leading away onto the distance.
I generally use manual settings when shooting with s DSLR or MILC. But with this phone, I frequently just let its automation make all of the decisions. It can do amazingly well, thanks to the high level of computing power in the phone.
It's annoying how well the fully auto shooting works, actually. If you've been a photographer for a long time, you will understand what I mean by that! My years of experience, learning, and skill are well-simulated by the program in this phone!
What next? The phone will do the composition, too? At least for the moment, I'm still needed for that, I guess.
Edit to add:
Remember that you can touch a place on the screen to activate the focus tracking or select the point where you want the camera to focus. As with any autofocus system, you need a way to tell it where you want to focus. The camera cannot read our mind, well, not yet, anyhow! So do use the touch screen to choose the focus point.
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