Rather than allow your camera to choose it's own focus area using focus 'auto-area / grid area', you'll get far more consistent results if you just use one focus area that you have control over. But depending on your camera, you may not be able to get out of the auto area / grid area mode unless you first get out of the 'full auto-mode' and switch to Aperture Priority, Shutter Speed priority or the 'P' mode.

Once you've done that you should have a focus area in the dead centre of your viewfinder or LCD screen, it normally lights up when you half press the shutter. But, just like in the above photo, what if your main subject is not in the centre, or you want to use the rule of thirds for a better composition?

'Focus and re-compose' to the rescue
All you need do is place the focus square on your main subject, and half-press the shutter. That will lock the focus and exposure. Then, keeping the shutter half-pressed, re-compose so that your subject is now in the correct position in the frame.

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Many photographers use the 'focus and re-compose' technique all of the time, it's very simple to do and generally very accurate. But it can fail under some circumstances, if you're shooting at wide apertures and have a very shallow depth-of-field, when you re-compose the subject may no longer be on the same plane of focus, and so will not be tack sharp. In that case, just use one of the camera dials to move the focus area square over the subject, like in the photo at the top of the page. The actual mechanics of moving the focus area varies depending on the camera, if you can't figure it out, just consult your manual.

Nesting black swan, taken using 'focus and re-compose' at f2.8

Nesting black swan, taken by moving the focus area

Comparison of the two photos.

Watch the video on this very subject here