All digital cameras that have an Auto Mode have Auto Focus (AF). You press the shutter release half way down and the camera focuses on the subject then press the shutter release the rest of the way to take the picture. Auto Focus is an amazing step up from film cameras because it allows you to shoot one handed and not have to use your other hand to focus with.
The downside to AF is that sometimes it just won't focus on subject you want. This usually occurs when you are shooting something up close and what you want to shoot is surrounded by a bunch of other stuff like flowers and leaves and the camera seems to like the background better.
One way to get around this is to isolate your subject by holding your hand or putting a piece of paper behind your subject. Press the shutter release half way down and let it focus on your subject. Once you have the proper focus, without letting go of the shutter release, remove your hand or paper and take the picture.
There are other ways to help your camera focus on what you want to shoot using various focus modes.
My Sony Cybershot, DSC H5 has 4 modes:
Multipoint - used for pictures with a lot of points of interest.
Center - used for shooting a specific area or subject.
Flexible Spot - allows you to focus in specific areas.
Manual - you do the focusing.
Find in your manual the focus modes and where to access them on your camera and reply to this thread with the kind of camera you have and list the different modes of focus for your specific camera.
Spend the week with your camera manual and camera and learn how to use the different focus modes and get to a point you don't have to consult the manual on how to access them and can readily switch focus modes specific to what you are shooting. Try shooting the same subject using all the modes and see if there is any difference.
