I've had a D3200 for a quite a while now, I started on a D3100. I did a lot of reading, mainly on the basics of photography such as previously mentioned the exposure triangle, and how to operate my camera. After an initial try out in auto, I went to A and S mode, mainly Aperture for the type of shots I prefer. Now and for the last few months I try to alwys shoot in manual mode, this costs me more waste shots (more to think about, more mistakes initialy), but I am learning more about the mechanics of getting a good shot and the practice help you look at a scene and start estimating your settings before you shoot. I also have to take more time over a shot, so instead of point and shoot you look at both the settings and the scene in more detail. it can be a frustrating way to work as often things just do not work out, always my fault, wrong settings through rushing usually, but when you do get a good shot it is how you envisaged and it does give you a buzz. I shoot in A or S when I dont have the time to set things up such as photographing the cats (most unco-operative models, worse than the kids, they'll model for McDonalds!).
I also shoot exclusivly in RAW and use Lightroom 4 for nearly all my post shoot processing. I have Elements as well but never seem to find the time to use it, and I am still learning the power of Lightroom, the Adobe videos are a good starting point, I also have the complete Adobe course that I bough that I am going through.
If you want to look at some photos taken with a D3200, my Flickr link is almost exclusivly D3200 shots.
Most of all, have fun and enjoy it, even when shots go wrong, look at the data and work out what went wrong, then the next time you are shooting a similar scene, you will be more likely to get it right.
Over the past year or so I have gone from shooting 50-200 shots, to shooting 10-30, but spend more time planning, and instead of 200 mediocre shots, I will get 3-10 shots that I ma happy with to process further, and from these will probably reject another 50%, saving only the best permanantly.