Want to get more high quality candid and action flash photos from greater distances when using your built-in flash? That scenario may sound like a mouthful, but it's one we all face on a regular basis as hobbyist photographers for a couple of reasons.
First, because the range of built-in flashes is typically only 4 to 5 meters for point-and-shoot cameras (a little more for most SLRs) and we can't always get that close, especially when shooting action. Second, because reducing shutter speed to let in more light isn't an option for candid and action shots where poses aren't being held for the camera.
Many point-and-shoot cameras allow for more powerful attachable flashes that extend the range and flexibility of your flash photos, but most shots are still taken without one. You can work around this issue by knowing your built-in flash range, becoming familiar with judging the amount of available light, and being ready to increase your ISO. (This tip also works for SLR shooters who regularly shoot without their external flash.)
Here is a series of example photos that will help demonstrate this useful technique. Our subject is a bouquet of flowers set in a room dimly lit by daylight through the windows, but let's pretend it's a child at play in a poorly lit room or outside on a dark day. The point-and-shoot camera (a Canon PowerShot A70) has been put into manual mode and been set to a shutter speed of 1/500 with an aperture of f/4.8 to catch action and non-posed candid expressions. To begin, you leave the ISO at its default of 50.
Let's start with an example where you are nice and close to your subject, say within a meter of your child playing on the floor. The first example (Fig. 1) shows a bad overexposure shooting from within a meter of the subject with a full flash setting. In this case, you quickly adjust your flash strength to compensate. The second example (Fig. 2) is a nice exposure from the same distance using a flash strength of three quarters. So far so good.
Fig. 1 
Fig. 2 
Click any photo for a larger example.
Now your subject takes a few steps away to about 3 meters distance. Without adjusting your flash strength, which is still at three quarters, you continue to get a nice exposure (Fig. 3).
Fig. 3 
Then your subject moves to about 4 to 5 meters away oops, your flash is still at three-quarter strength (Fig. 4) resulting in an underexposure: a quick bump to full strength and you're back to good photos (Fig. 5).
Fig. 4 
Fig. 5 
Now your subject ranges to about 6 or 7 meters away and you either don't want to or are unable to move closer. Your initial settings and your return to full flash aren't getting it right anymore (Fig. 6), so you bump the ISO to 100 and it is still not there (Fig. 7). Another nudge to 200 ISO is better but still dimish (Fig. 8). A final nudge to ISO 400 (Fig. 9) -- the top setting for the Canon A70 and many digital point-and-shoots -- and the exposure is acceptable again, but you start to see some noise.
Fig. 6 
Fig. 7 
Fig. 8 
Fig. 9 
So, by upping your ISO to compensate for your weak built-in flash you now have two successful candid/action photos from 6 to 7 meters from your subject. Neither is quite as nice as the ones taken from within the range of your built-in flash, but they are both acceptable and at least you have the photo rather than a picture with murky outlines only.
The photo from 6 to 7 meters at 200 ISO (Fig. 8) is close enough to the mark that you could easily adjust the light levels in your editor to make up the difference (Fig. 10).
Fig. 10 
In similar fashion, the photo from 6 to 7 meters at 400 ISO (Fig. 8) is good but shows a bit of noise - noise that can be filtered out in your editor (Fig. 11).
Fig. 11 
The fixed photo in Fig. 11 above still shows some noise, but it is significantly less noisy than the original. Your choices here (with the capabilities of the Canon PowerShot A70) are: to not get the shot at all once you are out of range of your built-in flash; to get it by bumping up your ISO to 200, and then to make final adjustments using your editor's exposure tools; or, to crank up your ISO and remove noise later.
How much noise your digital camera adds as you increase ISO depends on your model. Having learned about this camera from the examples above, I would choose to still underexpose by a smidge, then "push" the photo in an editor. See Related Articles below for more information on "pushing" exposures and cleaning up ISO noise.