The most important thing to do is to reduce the exposure (EV, ISO, shutter speed, and aperture if your camera supports that).
If you can do that, then you can also try firing your flash (yes, add more light). When used this way it's called a "fill flash", and the idea is to raise the brightness of the areas in shadow. When you do that and reduce the overall exposure, you'll get a more balanced picture with less hard shadows.
However, you're at the mercy of your flash here; I doubt most point & shoot cameras will have enough flash power to really compensate for the outdoor light. And that's assuming your camera can reduce the exposure enough to begin with.
This is where SLRs stand out; they give you more control over what you can do. They also tend to support hot-shoe flashes, which are bigger and more powerful.