Check that the camera lens is clean. Clean it using a soft cloth intended for that purpose, and do not scratch the lens.
When you enter a normal room temperature after being in cold weather, moisture can condensate on the lens. To prevent foggy photos in this situation, clean the lens before using the camera.
Keep the camera stable when taking photos, especially when taking photos in low light. Learn to press the camera key without shaking the phone. If you use the capture icon (the icon with the camera on it) on the touch screen, learn how to lift your finger without shaking the phone.
With fast moving targets, you can try to manually adjust the shutter speed to faster and/or adjust the ISO higher. This enables fast shutter speed.