Before you start spending more money, start taking photos. For the most part it'll be obvious what extras you then need (or the experts here can advise you based on the problems you encounter.
If you find yourself running low on power on a full days shooting - get a spare battery
If you run out of memory - get another card
If you find yourself wanting to zoom a little bit more - get a Nikon 55-200VR
If you find yourself wanting to zoom a LOT more - get the Nikon 70-300VR
If you want to be able to focus a bit closer, consider a semi-macro lens (eg Sigma 70-300 APO DG macro
If you keep hitting the wide end of the kit lens and want to go wider - get a 10-20 or 12-24 ultrawide zoom
If you want to shoot portraits, or want to shoot in lower light, get a Nikon 50mm f1.8
If you want to be able to focus a LOT closer, get a dedicated macro lens
If you use flash a lot, consider an SB600 flashgun
If you use macro, long non-vr lenses, or work in low light (or just want critically sharp photos) - get a decent tripod
As stated earlier - if you have shed loads of cash - just run out and get all of the above, but otherwise wait until you find youself cursing something and the next wallet emptying object of desire will become obvious.
I'll second the recommendation for Nikon Capture NX and Photoshop Elements. You can rarely rescue a bad photo, but you can routinely turn an 'OK' one into something quite stunning with 5 minutes of post processing.
I'll also second Brammers' comments - go out and play. Take hundreds of photos. You'll learn that DSLRS have limitations:
how low the shutter speed can be before you get camera shake
how fast the shutter needs to be to camera fast moving objects
how high you can push the ISO setting before the photo becomes a fuzzy mess
how much of the scene do you need in focus
etc etc
It's trial and error (mostly error at first). If you have the time and patience, the best way is to pick a subject and then try lots of different settings, then look at the results on your PC, and figure out which one worked best, and why. Post 'em here and we'll be happy to scratch our heads and try to help