If you're relatively new to the whole camera thing, you're probably using scene modes or even the full auto 'green' mode present on many cameras. The level of control afforded you in these modes varies, but they all have in common that they will tell you what decisions regarding shutter and aperture they have made, but tend not to allow you to change them. Some allow ISO adjustment, some don't. I would therefore argue that one of the best ways to learn how to take pictures is to find out what the scene modes do, then make those decisions or break those rules as you learn.
I should qualify this with one quick note. The actual decisions taken by the camera are way more complicated in many cases than I'm about to suggest. My description is more of an approximation or ultimate simplification of reality. The camera will usually use a clever metering mode, compare its results against a library of saved 'standard' scenes, and choose what it considers to be the best selection of variables. You (I presume) don't have such a library, so you'll be using rules of thumb mostly instead.
Landscapes
The landscape mode will be attempting to get as much in focus as it can. It will therefore be using the smallest aperture it can get away with whilst maintaining a fast enough shutter speed to give some chance of avoiding camera shake. If auto-ISO is enabled, it may increase the sensitivity to achieve the two aims. Some compact cameras lock the focus distance on infinity in landscape mode, then rely on their relatively high depth of field to make the foreground look acceptable too.
Portrait Mode
In many ways this is the opposite of landscape mode. The camera will select a large aperture (small number) and will usually be focussing pretty close. The aim is to blur the background, thus emphasising the subject. ISO will be kept as low as possible, while maintaining hand-holdable shutter speeds. This is easier in this mode due to the wide aperture in use.
Close-Up (macro) Mode
True 'Macro' photography is defined as producing an image on the sensor which is larger than life-size. This requires specialist gear and is not what the 'close up' mode is designed for. However, the principles are the same. This mode will be expecting you to be focusing as close as you can, often using flash to add light and allow the use of small apertures to maximize the extremely shallow depth of field at close range. Shutter speed is considered to be of secondary importance although at this range, any shake at all will make the picture unusable unless the light is bright enough to allow very fast speeds. The camera will therefore play its usual game of compromise and trade some depth of field for a safer shutter speed for handholding.
Night Portrait
Usually shown as a person's outline against a night sky on the mode dial, this is a mode which allows the use of a relatively advanced feature - slow sync flash - within an easy to use 'beginners' mode. The camera will meter so as to expose the dark scene properly, as if the subject person was not present. With this part out of the way, flash will be added so as to give extra emphasis to the subject, lifting them out of the darkness of the scene as a whole. Due to the potential slow shutter speed needed, this mode may well require the use of a tripod. Think of it as landscape mode (maximising depth of field for distant scenes) combined with a blip of flash. This mode will provide the means for you to get snapshots of family or friends or whomever, in front of darkened scenes such as night cityscapes or fairgrounds. Once you move on to manually controlling your slow sync flash, you'll find it's usually quite customisable for more natural results than the 'stuck on' effect that some auto modes create.
Sport/Action
This one is all about shutter speed. The camera will do its usual compromise calculations to work out how to get the fastest possible shutter speed without making the image unusable. It will do this by opening up the aperture as wide as it can, increasing ISO in some cases etc. It will sometimes also affect the focus mode, changing it from 'one-shot' to 'servo' or 'continuous' autofocus, meaning that there is no longer any concept of locking on - the camera will be expecting you to track the action, shooting as you follow. It will therefore follow as best it can by keeping the AF moving with the subject.
DEP and A-DEP modes (canon only)
if you have a canon SLR then you may well have access to one of these modes, and sadly there's a good chance that it will be A-DEP - the less useful of the two. In this mode the camera attempts to choose an aperture and a focus distance which will render the subjects under the closest and furthest focus points (in the viewfinder) sharp within the depth of field available. DEP mode is much more useful (though still hardly an everyday staple in my experience), allowing you to individually select, using the shutter button, the closest and most distant objects you want to be sharp, then allowing you to recompose before the shot is taken.
