When I got mine (D40 - predecessor to the D3000) I first show mostly in Auto mode or the scene selection modes. But I wasn't happy with the results. I did three things to make my pictures better (nothing like tyfliers) but I'm happy with how they've started turning out.
- Read a lot on photography. Prior to my DSLR I'd only messed around with point and shoot. I knew nothing about aperature, shutter speed, ISO, exposure compensation, white balance, etc etc. So I read up on them in books about general photography and books specifically for my camera. This helped me better understand how each setting would affect the picture, which leads me to number 2...
- I switched from auto mode to manual mode and would just take lots and lots of pictures of the same thing to see how each setting affected the picture. I might start in auto mode, note all the settings, then switch to manual mode and start with those settings. Then I'd take several pictures. Then I might adjust ISO, take several more pictures. Then adjust ISO more, take more pictures. Then I'd set ISO back to 'default' and adjust aperature, take pictures, adjust again, take pictures, you get the idea. I did this a lot just by messing with one setting. Then I'd mess with two settings, and look at how the affected each other. And I just kept messing around until I started getting pictures how I wanted them. I also did this with different light sources (including adjust white balance) such as indoors, outdoors, cloudy day, sunny day, etc. I thought about signing up for some classes, but figured I'd save some money and just figure it out by trial and error. Now I'm still no pro or anything, but I shoot exclusively in manual now. Sometimes it still takes me several "tries" to find correct settings, but I usually do and the usually still end up turning out better than shooting in auto. Like I said, I'm no expert or pro, but I'm happy with my pictures which is all that counts IMO (whereas before I was like you, I was bummed that I spent this money and pics weren't any better than my old P&S).
- Lastly I got an external flash and a tri pod. The pop up flash is garbage, especially for indoor shots. You really want something more powerful and flexible that allows you to bounce the flash. This will better light up your subjects and won't light them up harshly like the direct flash will. Especially if you're shooting in doors. I went with the SB-400. Much cheaper than the SB-600 which was more flash than I needed or wanted to spend $$ on). And the tripod really helped for taking pictures of snakes. I use the tripod and also bought the remote for the camera, this way I can have the camera set up ready to go and focus more on manipulating the snake. Before I'd get the snake posed and by the time I got behind the camera and all set it would have moved. With a tripod and remote, you can set the snake, then just move your hadn out of the frame, and use the remote to take a quick pic.
Also, take lots and lots and lots of pictures. The more pictures you take of something, the better chances you'll have of getting a good picture. I might take 20 pictures of a snake, and only get 1 or 2 that I'm happy with. Along those lines, only judge pictures by looking at them on your computer. The LCD isn't that great. It's good for setting exposure, etc, but often details aren't visible on it and sometimes pics that look good on it don't on a computer and vice versa.
I know you've already spent a lot of $$, but really consider an external flash. Many will say avoid the SB-400, but for probably 90% of people its plenty. It's one of those things that now that I have it, I don't know how I went without it.
Here are just two examples of the same snake taken several months apart.
Shooting in auto mode with built in flash (before I shot in manual and without SB-400 and tripod and remote). Note the "harshness" of the flash you can see reflected on him. He's also moved out of frame since I posed him:
Same snake taken using SB-400 bounced flash, tripod, and remote. You can see his colors look more natural and he looks lit up but doesn't have those harsh highlights. Also I was able to pose him and use the remote/tripod to snap this picture before he started to move away (though the camera focused on his body, and not head, so his head is slightly out of focus):