1) Don't use zoom! The photo quality is better if you take a photo zoomed out and then crop it in after.
2) Play with your settings! Almost every phone now has a dozen or so settings that you probably have never looked at. Take the time to get familiar with your phone (especially contrast, brightness & quality controls)
3) Get low! You don't always need to be standing when you take a shot, so try kneeling down, ESPECIALLY for photos of your kids! The closer to the ground you can get, the more depth in your picture. Experiment with an interesting point of view.
4) Find natural light opposed to the flash. A cell phone flash is the same as a built in camera flash- no good! They're harsh and often lack quality colour. You're better off to move your subject into natural light if it's available!
5) Remove distractions! It's important to simplify the scene of your photo as much as you can. If you're taking photos of people, make sure they're not wearing any distracting patterns or logos. If you're taking landscape, crop out man made landmarks. Be mindful of what is in the frame!