Moving subjects are more challenging to focus on than still subjects. In fact, no focusing strategy will get you guaranteed good focus for a subject moving quickly towards the camera. Depending on the circumstances, there are three strategies I use to focus on a moving subject. These options aren’t available for all cameras. I doubt any point-and-shoot cameras have the necessary features.
One option is to anticipate where your subject will move to, lock your focus on that location (using autofocus lock or manual focus) and then shoot the picture when your subject (hopefully) arrives in the right place. This is a good strategy when it is clear where your subject will be, such as a race car moving around a track. I used this strategy for the jumping lynx shot below. However, because I was laying on the ground and the lynx was jumping up in the air, I had to account for the additional vertical distance. So, I chose a location several feet past the jump-off point of the lynx and focused on that spot in the ground.
Caracaol (lynx) jumping to catch a piece of food
Secondly, if your camera has the option, you can use an auto focus mode which continuously tracks a moving subject and keeps it in focus. On Canon, this is called AI Servo. On Nikon, it is called AF-C. After setting the camera to the continuous focusing mode, you hold the shutter down half-way and keep the moving subject over the active focusing point in the viewfinder. The camera will continually keep the subject in focus. I used AI Servo on the cheetah shot below. Check your camera’s instruction manual for full details on this.
Close-up of a cheetah in a field in Namibia
Third, for slower moving subjects moving across the scene (rather than towards the camera), I often keep the camera autofocus mode set to the standard one shot (Canon) or AF-S (Nikon) and simply shoot right after locking focus. This is not a good strategy for fast-moving subjects, though.