The best thing I could recommend is to turn on some more lights. Especially if your pictures are turning out too dark or grainy. In low light, the iPhone seems to compensate by turning up the gain. Unfortunately, you don't have much control over the ISO or any other settings.
Before you take the picture, tap the screen where you want the phone to focus. From what I can gather from using my iPhone 4 is that by tapping the screen, the iPhone will usually do an additional meter for light, which usually helps my pictures.
If you're using the HDR function, this basically snaps 3 photos. One a normal exposure, one overexposed and one underexposed, then combines the image for what we hope to be a better result. Sometimes HDR photos turn out better, and sometimes worse. Experiment with tapping the screen at different points in order to adust how the shot is metered for light and exposure, and see what kind of results you get. I have found that metering on brighter areas usually leads to a better HDR image overall.
There are also some additional Apps you might want to look into picking up, like Camera+, which will give you some extra control, but one thing to remember is that the iPhone isn't a DLSR, and even though the iPhone's camera is still pretty good, it still doesn't match up to many basic point and shoot cameras as far as control goes. As far as cellphone cameras go, it's still pretty much tops.
I do quite a bit of photography myself. My primary photo camera is a Nikon D70, but I just got a D7000 and and still getting used to it. Anymore though, for daily point and shoot, I usually just pack my iPhone 4, but for doing anything more complex, I definitely rely on my Nikons.
I wish you luck, and happy shooting!