I would say practice, set the camera for the highest quality file option and get it off full auto. Set the ISO-speed manually and try to keep it as low as possible. Also if you need to get some kind of gear. Get a good quality tripod. Don't get one of those filmsy wobbly crap tripods, but a quality tripod that will hold a dslr. One tripod I can recommend is a Redged RTT-327, and a Vanguard SBH-20 ball head. Remember that a good tripod will follow as you progress in your photography, and the tripod set-up I've given you here will also hold a consumer DSLR like a Nikon D3200. Tripod Legs: [link] Tripod head: [link] When you fell you've outgrown your present camera, go for a good DSLR. But if you want to be serious with your photographic hobby, then I don't there's no way besides a good DSLR, and a good kit lens for start.
I had the same problem when I started but honestly yes it's practice that makes things better. Just play around with the iso, shutter speed and aperture in different light settings until you find the best for all (write down each as you go along. e.g if you find that a certain shutter speed works well for a certain setting write down the info and note what photo it was)
Everyone here gave great advice, two of the last three, gave the best, practice. I'm also an amateur, who basically hopes for a good picture. I have gone into manual. Actually, only shooting on manual now. It's not easy. Every shot needs new input from you, Exposure, focus, aperture, and framing. That's a lot to think about, when you just want to shoot that little puppy, quickly. (And don't forget about white balance, ISO, bracketing, etc) I practiced, most of the winter. Not sure if I learned anything, because we had a dark, cloudy winter. I got a lot of noise. Once I can sit outside, without freezing, I plan on taking a series of shots, of the same subject, using all of the different manual settings. I also plan on taking notes of each shots settings, so I can figure out how to take a picture, a certain way. Good luck. BTW I had an EasyShare z12 IS. It took fine pictures. [link]