Ever notice that when you take a flash picture, your subject is properly exposed but everything else seems too dark? It's a common problem and there is a solution. You need to increase the amount of non-flash (ambient) light in your picture.
The illuminating power of a light (like your flash) decreases rapidly the further out the light goes. As the light gets further from your flash, the area it lights up grows both in width and in height. It doesn't take long for the light from the flash to get so spread out that it has lost all of it's punch. If your subject is 10 feet away from you and the background is 20 feet away, the background is getting about 1/4 the amount of light as your subject. Because of that, your subject looks OK but the background looks too dark.
Here's an example:
This shot was taken at ISO 400, f/9, and 1/250 second. If I wasn't using a flash, the camera would have used ISO 400, f/9, and 1/15 second. In other words, I the shot above is underexposed by 4 stops (1/250 -> 1/125 -> 1/60 -> 1/30 -> 1/15) and the flash is compensating.
To improve the shot, I need a to keep the shutter open longer. Here is the same shot at ISO 400, f/9, 1/60 second. Now it's still somewhat underexposed, but it's much closer to the non-flash exposure. The background is much lighter but my subject is still lit by the flash.
So your next question should be, how to I control the mixture of flash and ambient light. There are several ways to do it. I find the most straightforward way is to shoot in manual exposure mode with the flash in E-TTL mode (or whatever your flashes auto mode is). I manually set the exposure to a stop or two less than what the meter reads and let the camera automatically set the flash level.
On Canon SLRs, you can also use AV mode. By default, if you take a flash shot in AV mode, the camera will try to automatically mix the flash and ambient light. This explains why, when shooting in AV mode, your camera sometimes picks ridiculously long shutter speeds for a flash picture. I think (correct me if I'm wrong) that Nikon's do the same thing in TV mode.
Now you might be wondering why the heck you would even bother with the flash if you were going to expose at or near the meter reading. There are several good reasons. First, if your background is reasonably well lit but your subject is not, the flash gives you some balance. The flash is very fast, so it freezes the subject (as long as they are staying reasonably still) even though the exposure is longer. It's also useful when you can get
close to a usable shutter speed and need just a bit more light.
Several years ago, I was shooting a reception at a restaurant. The ceilings were way too high and dark to bounce the flash. The room was also very large. Even at ISO 1600, my meter was giving me shutter speeds around 1/8 to 1/15 wide open. That's just too darn slow for shooting people. I didn't want to just blast people with the flash and lose my background. My compromise was to shoot at 1/30 and 1/60 (depending on how animated the subjects were) and let the flash fill the rest.
A good (but very, very old) Disney example is this shot near the Anti-Gravity Fountain. It's a scan of an old film shot, so I don't recall the exposure settings. The flash froze my still subjects (but not my flailing son) and the long exposure gave the fountain time to expose properly.
Another good use for dragging the shutter is to let moving lights show up as light trails in the picture. Here is a 3/10 second shot of a cast member playing with some lighted ball toys. The flash illuminated and froze (mostly) her while the longer shutter speed gave the balls a chance to draw trails. This technique is great for kids with waving sparklers or flashlights.
Another important consideration when dragging the shutter is whether to use first or second curtain sync. This refers to whether the flash fires at the start of the exposure (first curtain sync) or the end of the exposure (second curtain sync). The default for most cameras is first person sync, but it should probably be second curtain sync. I recommend that you change yours to second curtain and only flip it back for exceptional cases.
To understand this better, think of a picture of a car driving by at night. Your flash illuminates the car and the cars headlights form a light trail through the picture. With second curtain sync, the car is at the end of the light trails because the flash illuminated it at the end of the picture. With first curtain sync, the car would be light and then the light trails would extend out in front of the car. While neither looks like what we saw, having the light trails showing where things were
before the flash froze everything makes much more sense than the opposite.
The only example of when I'd use first curtain sync that jumps to mind is when shooting people. It might be easier to tell them to stay frozen for a second after they see the flash than to explain that they should stay frozen for a second before they see the flash.
OK, is this clear now? Try taking a flash picture in a relatively dark environment. Then switch to manual and adjust your exposure so that you are under the meter reading by only one stop. Now take the flash picture again. Compare the results. Try some shots further over or under exposed and see how they look. Obviously, it helps to have a tripod for longer exposure shots.
So how does this apply to people with P&S cameras? I've got no clue. If you have one, try experimenting with the flash in manual mode and see how it works.