Like the Levels command, the Curves command allows you to adjust the tonal range of an image. However the range and quality of adjustment is much greater. Levels is similar to using a hatchet, Curves is more scalpel-like in its precision.
The Levels command limits adjustments to just three variables, highlights, shadows and midtones. With the Curves command, you can adjust any point along a 0 - 100% scale while keeping up to 15 other values constant.
Before using the Curves command if you are in RGB or CMYK mode, go to Image | Mode | and select Lab Color . Adjustment of tonality levels can be done in other color modes, but artifacts and color shifts can result, especially if your monitor is not well calibrated. When you are done editing the tonality you can return to your previous image mode.
While editing your image, open the curves dialog box. Image | Adjust | Curves. See the dialog box on the right. The channel should be set to Lightness.

The horizontal axis of the graph represents the original brightness values of the pixels (Input levels); the vertical axis represents the new brightness levels (Output levels).
In the default diagonal line, no pixels have been mapped to new values, so all pixels have the same Input and Output values.
For Lab Color or CMYK images the curve displays percentage values from 0 to 100, with the whitest highlight (0) on the lower left. The darkest shadow (100) is on the upper right.
For RGB images, Curves displays brightness values from 0 to 255, with the shadows on the left.
While it is possible to use many adjustment points, usually only three are needed! The software automatically controlling most scanners tries to make the world a mix of midtones as shown below. No tone too black, no tone too white, all tones just right.

Start by moving the crosshair cursor to point C and clicking to establish an anchor/drag point. This point will be used to adjust the quarter-tones or highlights. Then move to point B, click and establish a mid-tone anchor/drag point. Finally move to point A and establish a three-quarter-tone or shadow anchor/drag point. See the figure on the right.

Make sure you have the preview box checked at this point so you can see the changes

Highlight a drag point by moving the cursor over it and clicking. Pull it down while watching the highlights in your image. Clouds if available are good visual reference points. Stop pulling when things are to your liking. Most midtones and all the shadows should remain unchanged. Be careful not to burn out the highlights by going too far.

The new tonality curve (see above) you've just created to enhance your image is called the S-curve. If an image is overly contrasty rather than flat the process would be reversed and the S would appear inverted. Simply pulling down on all three adjustment points would tend to lighten the overall image and is similar to increasing brightness with the Levels command, but much more precise. Likewise pushing up on all three adjustment points would tend to darken the overall image and is similar to decreasing brightness with the Levels command.