Hello TS! Welcome to CS!
Im a newbie too, got my D5000 last March. Your D3000 is a great camera for beginners too coz it comes with a 'Guide' mode that ask you what kind of pics you want to take then goes to the process of choosing the right settings. One way that I learn how to take pictures is by learning from the camera. I set to 'Auto' mode and each picture has the info settings when you transferred it to your pc. From there its just trial and error on which shutter, aperture, iso etc to set. Most of the time for now, my camera is set to 'P' mode, which I can vary the shutter or aperture, and play around with the other settings. Of course the best is to read up (which i did). Plenty of info on the net, books (library or stores) and magazines. I actually bought a 'dummies' book for the D5000 though im not sure if there is one for D3000. Anyhow, you can still get other references from other publishers. And there is always this forum page at CS
Happy shooting and enjoy your D3000!
Cheers!