|I'm assuming Photoshop here, but similar tools exist in almost all good editors...
First, adjust levels. Move in the right-hand slider (white point) until it touches the far right side of the histogram. In some cases, you will see a samll peak at the right end of the histogram, usually from small bright highlights. You may elect to clip these by moving the slider to the left of the peak, but be aware that you will lose any detail in these highlights. Also be aware that there is nothing "wrong" with doing this if it your artistic choice to do so.
Second, adjust curves. To lighten, move the center of the curve upward. I find that often a slightly s-shaped curve (higher contrast) is needed to avoid a "washed out" look if the original was quite dark.
Third, use a tool or technique to bring out shadow detail. My personal preference is the Photoshop CS "shadow/highlight" tool. A Google search will bring up ways to acomplish the same thing manually. Use this sparingly, if overdone it is not pleasing.
Fourth, if required, run noise reduction on all or parts of the image if bringing up the brighness has resulted in visible noise.
Remember that what you are doing is "correcting" for underexposure; since you were underexposed, you have not used the full dynamic range of the sensor (or film). For this reason, you will have a lower signal to noise ratio, and your resutls will never be quite as good as if the photo was exposed properly to begin with. With a low-noise camera, however, the results of even a 1 stop correction can be quite good. Much more than one stop of correction usually results in marginal images.