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There are a few rules to remember. These are guidelines and not unbreakable, though.
-Always shoot with a speed that's the reverse of your focal length (in 35 mm equivalent). For example, if your camera is a 36-110 mm, and you shoot at full telephoto (110 mm), then you should use a speed of 1/110 or faster to avoid blur caused by yourself. The faster the speed, the least blur there will be.
-For a slowly moving subject (human walking, etc) a speed of 1/250 should be enough to stop the action. For a faster subject (human running) try 1/500. You might need to adjust those values if the subject is moving towards you, or away from you, or laterally.
-The larger the aperture (smaller f-number) the shallower the depth of field. For a landscape, use a small aperture. For a portrait, use a large aperture. Most cameras deliver their best results (sharpest) when you use an aperture between f4.5 and f5.6 but this depends on the lens. Those are simply the usual mid-values and that's where you get the least diffraction effects.
-Remember that generally, when you zoom the widest aperture decreases. So if you set your aperture to the widest at wide angle, then zoom, your aperture value will probably change.
Related readings:
Aperture and shutter
http://www.digicamhelp.com/difference-between-aperture-shutter-priority-modes/index.htmhttp://www.digicamhelp.com/cgi-bin/yabb/YaBB.cgi?board=working;action=display;num=1129303966Exposure
http://www.digicamhelp.com/learn/camera-techniques/control-over-exposure.htm