The great thing about digital cameras is that you can immediately see if the photo has turned out anything close to how you expected it to. If it looks a bit dark on the screen, I do one of the following (possibly all three, and then decide later which one I like best).
1) Dial up the exposure setting:
This is useful when you are indoors, but don't want to use the flash.
On my Nikon D70s, I hold down a little button with my finger (it has a +/- on it) and rotate the thumb dial. I can move the exposure up in halfs from +0.1 to +3.
This forces the camera to let in more light (basically by slowing down the shutter speed). It's worth bearing in mind that the shutter speed may slow to the pount where it becomes difficult to take a sharp picture.
2) Expose for the shadows:
I use this method when I want to brighten up parts of the scene which are a bit too far away for the flash to reach.
Rather than manually dialling the exposure up, you can force the camera to brighten up the shadowed areas. Zoom right in to the area you want brightened, and then lock the exposure (on my camera there is an exposure lock button on the back, which I press with my thumb). Then recompose and shoot.
In the scene below, using the flash would have lit up the leaves from the branch, which i didn't want to do. In fact, the first photo is probably fine, but a comparison of the two just demonstrates what you can do with the 'zoom, lock, recompose' method.
Remember that when you do this outdoors, the entire scene will be brightened, which may result in a washed out background. It's really up to you just how much you want those shadows lit up.
3) Fill-in flash:
If the foreground is close by and in shadow and the background very bright, you could use the flash.
On my camera I can manually adjust the amount of flash used (press the flash button and rotate the thumb dial), which is really useful.
In this photo I was on the edge of a steep slope, making it impossible to recompose out of the shadows.