I am new to photography, and need a little advice. I currently have a Samsung L83t.
To get rolling, where do I go from here? Does the camera matter? Is this camera enough to start with?
I think the most important thing I can say is to go out and take pictures.
Take the kind of pictures you want to take (not test, practice or drill pictures) and pay attention to what you are doing and what results you get from what you are doing (I could say "take notes" -- but that doesn't work for everyone). If you do that, you will be learning about Photography and doing Photography. Too often we get caught up in learning without doing.
Once you have taken enough pictures you will realize that you have been learning about photography and will eventually decide (well, perhaps) that you need a different camera to be able to more easily capture what you want to capture.
But -- fall in love what you do with you equipment, don't fall in love with your equipment (or worse, equipment you can't afford). I've shot with cameras typically considered "nice" or "high end" in the past and they haven't ever turned a junk shot into a fantastic one.
This might not be the best advice, but it is from the heart.
Welcome to photography!
Any camera is good to start with. Photography is more about the photographer than the camera, even if at some point you will find the limitations of a point-and-shoot like yours.
Take a look at this question about photography tutorials to learn the theory about light, composition, etc. and try out with your current camera.
I'll throw my take into the ring as well... The answers to your questions do depend on what kind of photography you're interested in. You didn't really say one way or another, so I suppose I'll make some assumptions about it such as that you don't plan on formal, studio, style photography. However...
So, is the camera good enough? Well, yeah, it is. If it generally takes a picture, then it's got something and it can be used. The camera is a tool and any camera is capable of doing good things given the right person controlling it. For example, I've seen the results of a fashion shoot using an iPhone and your camera is more capable than an iPhone. So, evidence that you have something to start out on and proof that it can even be done in a studio!
So, now that we've established that the camera can get you started, where do you start? Start by taking pictures, lots of them, but with a sense of what you're trying to convey. I wouldn't worry too much about the mechanics of the camera yet, just get comfortable with the idea of photography and let the camera deal with the mechanics for now. Focus on composing your images, capturing a mood, these kind of things. Don't worry if you end up with a bunch of dreck, we all do, tons of it too, since you can just toss them away and move on. This is a big advantage of digital, by the way, and you want to take advantage of it: it's not film. It doesn't really cost you anything extra to take the picture.
Now, after a while, you should look to start taking control of the camera as well. Learn to use the more manual modes on it and start controlling things like aperture and shutter speed, seeing what they do for you. There are questions and answers on the site about these things, but in a quick nutshell:
Finally, in all of that, read and try. Lots and lots of tutorials and demos out there on photography. Don't just read them, do them. Then, once you're well and truly hooked, go get a dSLR. :)
Also find time to study other photographers' work. You will see that everyone captures the moment/scene in a different way, and different equipment can make this and that possible.
But there is no best equipment or method, it's all about what kind of effect and message you want to display in your work. Everyone uses different tools, to tell different stories. Only time and experience will unveil what you're after.
I think you can learn enough about photography with your camera to find out if you want to pursue this further or not.
However, your camera imposes some limitations on the learning process: