(Article Updated November 2011)
Your autofocus, point-and-shoot camera most of the time will be able to produce very sharp images, however if you take a photo with the subject off-centre, so some of the background can be seen, for example, the camera may adjust to focus on whatever is in the background. The result is a blurred subject in front of a razor sharp background.
Use Focus Lock
The way around this is to use the camera's focus lock feature. Most models have one which is activated by half pressing the shutter release. Once your subject's in focus, keep the shutter depressed and recompose with your subject in its desired off-centre position.
You can also use the focus lock to ensure the subject has focused on exactly the right point of the subject. This is important for close up photography where it may not be possible to get the whole of an insect or flower in focus. In such cases pick the area that's most important and focus there. Where possible set a small aperture to ensure maximum depth-of-field.
The photo above shows what normally happens when you take a picture with the subject off-centre. The left hand shot has the subject blurred, but the background hedge is sharp. Using the focus lock on the statue has ensured it comes out sharp.
Sometimes there's not enough depth-of-field to allow all the elements within a photograph to be sharp. The left hand shot above shows the camera has focused on the joins of the tap, but the head is unsharp and this is very noticeable. By locking focus on the tap head the shot looks sharper, even though the connecting nut and rag are now blurred.
In the left shot above the camera has focused on the background trees. However, a quick focus lock on the flower ensured that it came out sharp against a very blurred backdrop.
You can also use the focus lock when shooting through a window to prevent the camera from being fooled and focusing on the glass. If you're on a coach or in the car, for example, lock the focus on the furthest point you can find and the recompose through the window.
Do make sure your subject doesn't move once you've locked the focus as any change in position (moving closer or further away from the lens) will mean your subject will no longer be in focus. If they do move, release the shutter button and repeat the focus-locking steps.
Beware some cameras lock the exposure at the same time as the focus. If so you have to be careful when shooting in tricky lighting because the exposure on the area that you are focusing on could be very different to the actual composition that you shoot. Some more advanced SLR cameras have an option to select the mode used for the AEL button so you can have focus lock and/or exposure lock selected.