Hmm, good choice on the Nikon D3100. One of the best entry-level DSLRs around. Anyway, on your question :
(M) - Manual : This allows you full control over the camera's settings, including shutter speed, aperture, ISO, white balance, exposure compensation, etc.
(S) - Shutter priority : This mode lets you decide what shutter speed you want, while the camera automatically decides the optimum aperture, ISO, etc for you.
Useful when shooting moving subjects. For example, you dial in a shutter speed of 1/500s to freeze a runner. The camera will then decide on optimum ISO and aperture settings to ensure a well-exposed shot.
(A) - Aperture priority : The opposite of (S). Here, you decide the aperture value, while the camera decides the other settings such as shutter speed, ISO, etc.
Useful when isolating subjects from background, such as food. Dial in a low aperture number, for example f3.5 (I assume you have the 18-55mm kit lens), and you'll notice that your subject is sharp whilst everything else in the background is blurred out. The camera will then assign an optimum shutter speed and ISO to ensure the perfect exposure for the shot.
(P) - Program Auto : A mixture of full auto and some of the above. The camera chooses most of the settings for you, whilst allowing you to input some of your own. You can use this if you're not very familiar with all aspects of the camera just yet, but still want to exercise some creative control.
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Just like in Navyfield, (M) or manual is still the best, as it allows you to be in full control of your photographs. It can be a little tricky at first, but once you master the basics, everything should come naturally.
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