Photography can be a very interesting hobby. I also has the possibility of becoming very expensive...if you let it. But you can literally start from anywhere.
Technique counts for so much of photography, and however I disagree a little with the fact that it doesn't matter what your camera is. You know there's the saying "A good builder never blames his tools"? Well what that saying doesn't say is a builder won't build a house without the right tools.
I suppose this is an industry problem, as photography became more affordable for the masses, they demanded an easier to use and cheaper device...through which the point and shoot has developed...it has killed the market for passionate photographers by giving control of things to a computer.
Depending on how simple or advanced your camera is you should be able to experiment with composition, and some basic exposure techniques. Join some photographic websites, and your local photographic meetup group (sometimes called flickrmeet or flickr group).
However you eventually will need to be able to take over a lot more control as you grow...so start saving...even if it's for a 35mm film SLR.