Congrats on your first dSLR! I still haven't gotten one yet.
With regard to shutter speeds: In short it's how long the picture is exposed. If this is longer, your picture will be brighter. The tradeoff is that your exposure is longer! If you are shooting something that's fast, it will blur. If you go below roughly 1/60th of a second, your photo will probably blur just from the shake in your hand, at which point you will need a tripod to do longer exposures. Faster action needs a faster shutter - running kids or shooting sports will need a short exposure.
Aperture: This is basically how far open the lens is. A perfect lens would be a pinhole, infinitely small. This lens could focus everything at once. This can't actually exist, so the closest thing is fully stopped down, which can focus most things. This is a very dark picture. The opening is measured in f-stops. I'm not sure how it works for dSLRs but for film lenses the smallest is usually f/16, f/22, or f/32. The tradeoff here is depth of field, how much is in focus, for light. Also, lenses are not at their best either fully stopped down or fully open. Keep them in the middle of their range for the sharpest and best picture, or open them up all the way to soften the picture (careful with the focus though!).
ISO speed: This is the "sensitivity" of the sensor/film. It's how much light it needs to expose the same amount of data. An ISO 800 film can expose twice as much in the same time as an ISO 400 film, and 4x as much as an ISO 200 film. The tradeoff here is grain. Film used to get grainy, and sensors do too. It will show up as light/dark spots in your image, google "ISO noise". You should be good up to ISO 800, 1600 will have moderate grain, and it gets worse from there.
To tie this all together: everything actually revolves around f-stops. Each exposure notch doubling the time doubles your light, this is 1 f-stop. For example, going from 1/250th of a second to 1/125th of a second gives you one f-stop increase in light. Opening your aperture one full stop gives you one f-stop. Doubling your ISO gives you an f-stop.
Now, basically you play a balancing game. You have a certain amount of f-stops to "spend". You can slow your shutter and try to have a wider depth of field, or try to use a slower ISO to get finer detail. You can increase your ISO to try and get a wider field of focus or a faster shutter. You can open your aperture to try and speed up your shutter or use a slower ISO.
Now, to make this still more complicated, if you save your RAWs (which you are,
) you can post-process and try to change things even more. You can do what's called "pushing" or "pulling". In film terms, this is shooting a film at the wrong exposure and under or over developing the film. You can push a picture and increase the brightness, possibly making the picture look right or getting extra detail in the shadows, at the expense of possibly "blowing" the bright areas. You can "pull" a shot and try to get extra detail out of the bright areas, darkening the picture and possibly losing detail in the dark areas. You can sort of do this in the camera by using the EV controls too, and I think this is supposed to be better, but obviously must be done in real time.
Someone tell me if I'm wrong on any of this, but I think it's a good place to start.