With my SX20 IS if you use flash, it'll actually make the photo darker
The only reason the photo is darker is because the flash isn't powerful enough to reach the subject.
When you use flash, the camera sets the shutter speed to a fixed value (typically 1/60 of a second, but it can be as fast as 1/250 or more on better cameras). When you shoot, the camera fires the flash and leaves it on long enough to capture the right amount of light to get a good exposure. The flash can only stay on so long, though. If the flash isn't up to the task, the picture will come out underexposed because of the quicker shutter speed.
If you can get close enough to the subject for your flash, you can indeed use it to add light to the scene. Even on a bright, sunny day, flash can be very useful for diminishing shadows and bringing out color on birds in the shade. If you can use an external flash on your camera (some P&S cameras have a hotshoe for an external flash unit), they're typically much more powerful than built-in flashes. Also, you can buy a flash extender (the "Better Beamer" is a popular one of these) for an external flash to get more range.