Probably the single most important photo-editing tool
When I start editing a photograph, this is usually he first tool I start using. Curves is strong and will make mracles on any photograph coming straight from the camera - as it will on almost any other picture you can think of.
In the curves dialog, you can place up to 16 points on the curve in order to manipulate specific areas of the tonal range of the photograph. The diagonal line represents the tonal range of the picture - as long as it´s a straight line going from bottom left to top right, it´s unedited.
In the above screendump the curve has been slightly adjusted - in this case the way many automatic point-and-shoot cameras do in-camera before storing the data on the memory card. But, as said, with up to 16 individual points marked on the curve, you´ll have unlimited possibilities to adjust your photo to your heart´s delight.
In the lower left corner is the black point. Proceeding along the curve toward the upper corner, after the black point are the shadows, then the midtones followed by the highlights and ending at the upper right corner with the white point. When you work on the RGB (Red, Green, Blue) composite channel, you affect both brightness and contrast. Colour balance can be adjusted working in the seperate colour channels.
Another way of adjusting contrast in this tool could be by using the 3 pickers at the bottom right. The left one of the three sets the black point when selecting it and then clicking somewhere on your picture you want to be absolutely black. Same procedure with the grey-point picker in the middle and again the white-point picker to the right. Don´t be afraid to experiment - everything can be undone.
If you want to adjust contrast and brightness in a picture - this is the best tool. Don´t even be tempted by the Brightness/Contrast "toy" that is a blunt and primitive instrument compared to the fine, almost surgical, precision of the curves tool.
This should get you started even if you haven´t tried this tool before. I would advice you, though, to work in a copy of the original photograph - should you make an irreversible error for some reason.